Hájek-Rényi Type Inequalities and Strong Law of Large Numbers for NOD Sequences
|
|
- Adela Kelly
- 6 years ago
- Views:
Transcription
1 Appl Math If Sc 7, No 6, Appled Matheatcs & Iforato Sceces A Iteratoal Joural Háje-Réy Type Iequaltes ad Strog Law of Large Nuers for NOD Sequeces Ma Sogl Departet of Matheatcs, Chao Hu Uversty, Chaohu, 38000, HeFe, P R Cha Receved: 5 Apr 03, Revsed: 8 Aug 03, Accepted: 9 Aug 03 Pulshed ole: Nov 03 Astract: I the paper, we get the precse results of Háje-Réy type equaltes for the partal sus of egatvely orthat depedet sequeces, whch prove the results of Theore 3 ad Corollary 3 K 006 I addto, the Marcewcz type strog law of large uers s otaed At last, the strog stalty for weghted sus of egatvely orthat depedet sequeces s dscussed Keywords: Háje-Réy equalty; egatvely orthat depedet sequeces; strog law of large uers Itroducto We use the followg otatoslet X, e a sequece of rado varales defed o a fxed proalty space Deote S = = X ad T = = X EX for each ad IA e the dcator fucto of the set A Háje ad Réy 955 proved the followg portat equalty If X, s a sequece of depedet rado varales wth ea zero, ad, s a odecreasg sequece of postve real uers, the for ay ε > 0 ad postve teger <, X P ax = ε ε EX j + EX j j= j=+ j I the paper, we wll further study the Háje-Réy type equalty ad the strog law of large uers for egatvely orthat depedet sequeces Defto A fte collecto of rado varales X,X,,X s sad to e egatvely upper orthat depedet NUOD, f for all real uers x,x,,x, PX > x,=,,, PX > x, ad egatvely lower orthat depedet NLOD, f for all real uers x,x,,x, = PX x,=,,, PX x 3 A fte collecto of rado varales X,X,,X s sad to e egatvely orthat depedet NOD f they are oth NUOD ad NLOD = A fte sequece X, s sad to e NOD NUOD Or NLOD,f every fte sucollecto s NOD NUOD Or NLOD Lea cf Bozorga et al, 996 Let X, e a sequece of NOD rado varales, f, f, e all odecreasg or all ocreasg fuctos, the f X, s stll a sequece of NOD rado varales Lea cf K, 006Let X,X,,X e NOD rado varales wth EX = 0 ad EX < for all The we have p E X + p EX+ 4 = = for all tegers, p ad + p Moreover, we have E ax X log 3 + EX 5 = = By Lea ad Lea, we ca get the followg Corollary Corollary Khtche-Kologorov theore Let X, e a sequece of NOD rado varales If VarX log < 6 the X EX coverges as Correspodg author e-al: 7879@qqco c 03 NSP Natural Sceces Pulshg Cor
2 50 M Sogl: Háje-Réy Type Iequaltes ad Strog Law Háje-Réy type equaltes for NOD sequeces I ths secto, we wll gve Háje-Réy type equaltes for NOD sequeces, whch prove the results of K 006 Theore Let X, e a sequece of NOD rado varales ad, e a odecreasg sequece of postve uers The for ay ε > 0 ad ay teger, P ax j= 4 ε log 3 + ε j= j Proof Wthout loss of geeralty, we assue that for all Let α = For 0, defe A =:α < α + For A /0, we let v = ax : A ad t e the dex of the last oepty set A Ovously, A A j = /0 f j ad t A =,,, It s easly see that α =0 v < α + f A ad X EX, s also a sequece of NOD rado varales y Lea By Marov s equalty ad 6 Lea, we have P ax t =0,A /0 j= = P ax ax 0t,A /0 A j= t P =0,A /0 α ax v ε α E ax ε t =0,A /0 ε log 3 + ε ε ε j= v j= α log 3 v+ j= Now we estate v j= t =0,A /0,v j t α =0,A /0,v j α Let 0 = : A /0,v j, the j v0 < α 0+ follows fro the defto of v Therefore, t =0,A /0,v j α < = 0 = α α α 0 < α = 4 3 α j j Thus follows fro ad 3 edately Theore Let X, e a sequece of NOD rado varales ad, e a odecreasg sequece of postve uers The for ay ε > 0 ad ay postve tegers <, 4 ε P ax j= ε + 4[log j= 3 +] j=+ j Proof Oserve that ax thus j= + ax + P ax j=+ j= j=, ε 4 P ε j= + P ax + j=+ ε By Marov s equalty, Lea ad Theore,4 ca e otaed 3 Marcewcz type strog law of large uers for NOD sequeces Theore 3 Let X, e a sequece of detcally dstruted NOD rado varales wth P X /p log < for 0< p< Assue that EX = 0 f p<,the X /p 0 as, 3 = Deote Proof Y = /p IX /p +X I X < /p + /p IX /p the PX Y = Borel-Catell lea Thus /p P X /p <, whch ples that PX Y, o = 0 y the X 0 as f ad = oly f /p Y 0 as So we eed to show that = c 03 NSP Natural Sceces Pulshg Cor
3 Appl Math If Sc 7, No 6, / wwwaturalspulshgco/jouralsasp 5 ad /p /p Y EY 0 as,, 3 = = EY 0, 33 By Corollary ad Kroecer s lea, to prove 3, t suffces to show that I fact, Var Y /p Y Var /p log < 34 log EY C P X /p log + C C+C log /p C = = = /p log EX I X p < EX I X < /p log /p log /p E X p X p I X p < C+C /p E X p p/p I X p < = < Hece 3 holds Next, we wll prove 33 It wll e dvded to two cases: If p =, y E X p < ad Leesgue doated covergece theore, we have l /p P X /p =0, 35 l EX I X < /p = l Ω X ωi X ω < /p Pdω = EX = 0 36 Thus, EY /p P X /p + EX I X < /p 0, as By the Toepltz lea, we ota l EY = 0 = If p, y the Kroecer s lea, to prove 33, t suffces to show that For 0< p<, EY /p C+C j= C+ EY /p < 37 P X /p + j= j= = j E X I X < /p /p /p E X I j X p < j /p E X I j X p < j j /p E X p j p/p I j X p < j< For p<, y EX = 0, we ca see that EY /p P X /p + C+ C+C j= j= j j= EX I X < /p /p /p E X I X /p /p E X I j X p < j+ /p E X I j X p < j+ j /p E X p j p/p I j X p < j+ < Thus 37 holds, whch ples 33 y Kroecer s lea We get the desred result 4 Strog stalty for weghted sus of NOD sequeces I ths secto, we wll study the strog stalty for weghted sus of NOD rado varales Frstly, we wll gve soe deftos as follows: Defto 4 A rado varale sequece X, s sad to e stochastcally doated y a rado varale X f there exsts a costat C, such that P X >x CP X >x 4 for all x 0 ad Defto 4 A rado varale sequece Y, s sad to e strogly stale f there exst two costat sequeces, ad d, wth 0<, such that Y d 0 as 4 Lea 4 Let X, e a sequece of rado varales whch s stochastcally doated y a rado varale X For ay α > 0 ad > 0, the followg stateet holds: E X α I X CE X α I X + α P X > Where C s a postve costat Theore 4 Let a, ad, e two sequeces of postve uers wth c = /a, c = /a log for ad Let X, e a sequece of NOD rado varales whch s stochastcally doated y a rado varale X Defe Nx= Card : c x, Rx= x Nyy 3 dy, x>0 If the followg codtos are satsfed: Nx< for ay x>0, R= Nyy 3 dy<, EX R X <, the there exst d R,,, such that = a X d 0 as 43 c 03 NSP Natural Sceces Pulshg Cor
4 5 M Sogl: Háje-Réy Type Iequaltes ad Strog Law Proof Deote X c = c IX < c +X I X c +c IX > c,, thex c, ada X c /, are stll NOD fro Lea Sce Nx s odecreasg, the for ay x>0 Rx Nx x y 3 dy= x Nx, 44 whch ples that EN X EX R X < Therefore = P X X c = P X >c = C P X >c CEN X < 45 = By Borel-Catell lea for ay sequece d, R, the sequeces = sae set a X c = a X d ad d coverge to the sae lt o the We wll show that = a X c whch gves the theore wth d = It follows fro Lea 4 that Vara X c log EX c 0 as, = EX c a EX c 3 P X >c +3 EX I X c C P X >c +C EX I X c CEN X +C EX I X c 46 EX I X c = EX I X c :c + EX I X c = I + I 47 :c > Sce N = Card : c R < fro 44 ad codto, the I < I = EX I X c :c > = = <c EX I X c N N EX I X = N N EX I X = + N N EX I< X = = I + I I C N N = = C j j= j+ 3 = j= N N j 3 C j+ 3 N j+ C y 3 Nydy< j= Sce Nx s odecreasg ad Rx s ocreasg, the I = = = = = N N EX I< X N N EX I < X = = EX I < X C = C C Therefore EX I < X EX I < X N N N + = Nxx 3 dx REX I < X EX R X I < X CEX R X < Vara X c = log < 48 followg fro the aove stateets By Corollary ad Kroecer s Lea, t follows that a X c EX c 0 as 49 Tag d = = a EX c,, the = We coplete the proof of the theore Acowledgeet a X c d 0 as Ths wor s supported y Foudato of Ahu Educatoal Cottee KJ03Z5 The author s grateful to the aoyous referee for a careful checg of the detals ad for helpful coets that proved ths paper Refereces [] Bozorga, A, Patterso, R F, Taylor, R L, Lt theores for depedet rado varales World Cogress Nolear Aalysts, 9, [] Chrstofdes, T C, Maxal equaltes for deartgales ad a strog law of large uers Statst Proa Lett, 50, [3] Fazeas, I, Klesov, O, A geeral approach to the strog law of large uers Theory Proa Appl, 45, [4] Ga, S X, The Háje Réy equalty for Baach space valued artgales ad the p soothess of Baach space Statst Proa Lett, 3, [5] Háje, J, Réy, A, A geeralzato of a equalty of Kologorov Acta Math Acad Sc Hugar, 6, c 03 NSP Natural Sceces Pulshg Cor
5 Appl Math If Sc 7, No 6, / wwwaturalspulshgco/jouralsasp 53 [6] Hu, S H, Che, G J, Wag, X J, O extedg the Bru-Prohorov strog law of large uers for artgale dffereces Statst Proa Lett, 78, [7] Hu, S H, Wag, X J, Yag, W Z, Zhao, T, The Háje-Réy-type equalty for assocated rado varales Statst Proa Lett, 79, [8] Joag-Dev, K, Proscha, F, Negatve assocato of rado varales wth applcatos A Statst,, [9] K, H C, The Háje-Réy equalty for weghted sus of egatvely orthat depedet rado varales It J Cotep Math Sc,, [0] Lu, J J, Ga, S X, Che, P Y, The Háje-Réy equalty for NA rado varales ad ts applcato Statst Proa Lett, 43, [] Praasa Rao, B L S, Háje-Réy-type equalty for assocated sequeces Statst Proa Lett, 57, [] Sug, H S, A ote o the Háje-Réy equalty for assocated rado varales Statst Proa Lett, 78, Ma Sogl receved the MS degree Statstcs ad Proalty fro Ahu Uversty 007 He s curretly a teacher Chaohu Uversty Hs research terests are the areas of Proalty lt theores c 03 NSP Natural Sceces Pulshg Cor
Complete Convergence for Weighted Sums of Arrays of Rowwise Asymptotically Almost Negative Associated Random Variables
A^VÇÚO 1 32 ò 1 5 Ï 2016 c 10 Chese Joural of Appled Probablty ad Statstcs Oct., 2016, Vol. 32, No. 5, pp. 489-498 do: 10.3969/j.ss.1001-4268.2016.05.005 Complete Covergece for Weghted Sums of Arrays of
More informationComplete Convergence and Some Maximal Inequalities for Weighted Sums of Random Variables
Joural of Sceces, Islamc Republc of Ira 8(4): -6 (007) Uversty of Tehra, ISSN 06-04 http://sceces.ut.ac.r Complete Covergece ad Some Maxmal Iequaltes for Weghted Sums of Radom Varables M. Am,,* H.R. Nl
More informationResearch Article A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings
Hdaw Publshg Corporato Iteratoal Joural of Mathematcs ad Mathematcal Sceces Volume 009, Artcle ID 391839, 9 pages do:10.1155/009/391839 Research Artcle A New Iteratve Method for Commo Fxed Pots of a Fte
More informationResearch Article Some Strong Limit Theorems for Weighted Product Sums of ρ-mixing Sequences of Random Variables
Hdaw Publshg Corporato Joural of Iequaltes ad Applcatos Volume 2009, Artcle ID 174768, 10 pages do:10.1155/2009/174768 Research Artcle Some Strog Lmt Theorems for Weghted Product Sums of ρ-mxg Sequeces
More informationStrong Laws of Large Numbers for Fuzzy Set-Valued Random Variables in Gα Space
Advaces Pure Matheatcs 26 6 583-592 Publshed Ole August 26 ScRes http://wwwscrporg/oural/ap http://dxdoorg/4236/ap266947 Strog Laws of Large Nubers for uzzy Set-Valued Rado Varables G Space Lae She L Gua
More informationAlmost Sure Convergence of Pair-wise NQD Random Sequence
www.ccseet.org/mas Moder Appled Scece Vol. 4 o. ; December 00 Almost Sure Covergece of Par-wse QD Radom Sequece Yachu Wu College of Scece Gul Uversty of Techology Gul 54004 Cha Tel: 86-37-377-6466 E-mal:
More informationStrong Convergence of Weighted Averaged Approximants of Asymptotically Nonexpansive Mappings in Banach Spaces without Uniform Convexity
BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY Bull. Malays. Math. Sc. Soc. () 7 (004), 5 35 Strog Covergece of Weghted Averaged Appromats of Asymptotcally Noepasve Mappgs Baach Spaces wthout
More informationA Family of Non-Self Maps Satisfying i -Contractive Condition and Having Unique Common Fixed Point in Metrically Convex Spaces *
Advaces Pure Matheatcs 0 80-84 htt://dxdoorg/0436/a04036 Publshed Ole July 0 (htt://wwwscrporg/oural/a) A Faly of No-Self Mas Satsfyg -Cotractve Codto ad Havg Uque Coo Fxed Pot Metrcally Covex Saces *
More informationOn Convergence a Variation of the Converse of Fabry Gap Theorem
Scece Joural of Appled Matheatcs ad Statstcs 05; 3(): 58-6 Pulshed ole Aprl 05 (http://www.scecepulshggroup.co//sas) do: 0.648/.sas.05030.5 ISSN: 376-949 (Prt); ISSN: 376-953 (Ole) O Covergece a Varato
More informationSTRONG CONSISTENCY FOR SIMPLE LINEAR EV MODEL WITH v/ -MIXING
Joural of tatstcs: Advaces Theory ad Alcatos Volume 5, Number, 6, Pages 3- Avalable at htt://scetfcadvaces.co. DOI: htt://d.do.org/.864/jsata_7678 TRONG CONITENCY FOR IMPLE LINEAR EV MODEL WITH v/ -MIXING
More informationQ-analogue of a Linear Transformation Preserving Log-concavity
Iteratoal Joural of Algebra, Vol. 1, 2007, o. 2, 87-94 Q-aalogue of a Lear Trasformato Preservg Log-cocavty Daozhog Luo Departmet of Mathematcs, Huaqao Uversty Quazhou, Fua 362021, P. R. Cha ldzblue@163.com
More informationExtend the Borel-Cantelli Lemma to Sequences of. Non-Independent Random Variables
ppled Mathematcal Sceces, Vol 4, 00, o 3, 637-64 xted the Borel-Catell Lemma to Sequeces of No-Idepedet Radom Varables olah Der Departmet of Statstc, Scece ad Research Campus zad Uversty of Tehra-Ira der53@gmalcom
More informationJournal Of Inequalities And Applications, 2008, v. 2008, p
Ttle O verse Hlbert-tye equaltes Authors Chagja, Z; Cheug, WS Ctato Joural Of Iequaltes Ad Alcatos, 2008, v. 2008,. 693248 Issued Date 2008 URL htt://hdl.hadle.et/0722/56208 Rghts Ths work s lcesed uder
More informationThe Arithmetic-Geometric mean inequality in an external formula. Yuki Seo. October 23, 2012
Sc. Math. Japocae Vol. 00, No. 0 0000, 000 000 1 The Arthmetc-Geometrc mea equalty a exteral formula Yuk Seo October 23, 2012 Abstract. The classcal Jese equalty ad ts reverse are dscussed by meas of terally
More informationPROJECTION PROBLEM FOR REGULAR POLYGONS
Joural of Mathematcal Sceces: Advaces ad Applcatos Volume, Number, 008, Pages 95-50 PROJECTION PROBLEM FOR REGULAR POLYGONS College of Scece Bejg Forestry Uversty Bejg 0008 P. R. Cha e-mal: sl@bjfu.edu.c
More informationSUBCLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH SALAGEAN DERIVATIVE. Sayali S. Joshi
Faculty of Sceces ad Matheatcs, Uversty of Nš, Serba Avalable at: http://wwwpfacyu/float Float 3:3 (009), 303 309 DOI:098/FIL0903303J SUBCLASS OF ARMONIC UNIVALENT FUNCTIONS ASSOCIATED WIT SALAGEAN DERIVATIVE
More information( ) ( ) ( ( )) ( ) ( ) ( ) ( ) ( ) = ( ) ( ) + ( ) ( ) = ( ( )) ( ) + ( ( )) ( ) Review. Second Derivatives for f : y R. Let A be an m n matrix.
Revew + v, + y = v, + v, + y, + y, Cato! v, + y, + v, + y geeral Let A be a atr Let f,g : Ω R ( ) ( ) R y R Ω R h( ) f ( ) g ( ) ( ) ( ) ( ( )) ( ) dh = f dg + g df A, y y A Ay = = r= c= =, : Ω R he Proof
More informationX ε ) = 0, or equivalently, lim
Revew for the prevous lecture Cocepts: order statstcs Theorems: Dstrbutos of order statstcs Examples: How to get the dstrbuto of order statstcs Chapter 5 Propertes of a Radom Sample Secto 55 Covergece
More informationON THE LAWS OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES
Joural of Sees Islam Republ of Ira 4(3): 7-75 (003) Uversty of Tehra ISSN 06-04 ON THE LAWS OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES HR Nl Sa * ad A Bozorga Departmet of Mathemats Brjad Uversty
More informationA Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming
Aerca Joural of Operatos Research, 4, 4, 33-339 Publshed Ole Noveber 4 ScRes http://wwwscrporg/oural/aor http://ddoorg/436/aor4463 A Pealty Fucto Algorth wth Obectve Paraeters ad Costrat Pealty Paraeter
More information. The set of these sums. be a partition of [ ab, ]. Consider the sum f( x) f( x 1)
Chapter 7 Fuctos o Bouded Varato. Subject: Real Aalyss Level: M.Sc. Source: Syed Gul Shah (Charma, Departmet o Mathematcs, US Sargodha Collected & Composed by: Atq ur Rehma (atq@mathcty.org, http://www.mathcty.org
More information= lim. (x 1 x 2... x n ) 1 n. = log. x i. = M, n
.. Soluto of Problem. M s obvously cotuous o ], [ ad ], [. Observe that M x,..., x ) M x,..., x ) )..) We ext show that M s odecreasg o ], [. Of course.) mles that M s odecreasg o ], [ as well. To show
More informationChapter 5 Properties of a Random Sample
Lecture 6 o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for the prevous lecture Cocepts: t-dstrbuto, F-dstrbuto Theorems: Dstrbutos of sample mea ad sample varace, relatoshp betwee sample mea ad sample
More informationUnique Common Fixed Point of Sequences of Mappings in G-Metric Space M. Akram *, Nosheen
Vol No : Joural of Facult of Egeerg & echolog JFE Pages 9- Uque Coo Fed Pot of Sequeces of Mags -Metrc Sace M. Ara * Noshee * Deartet of Matheatcs C Uverst Lahore Pasta. Eal: ara7@ahoo.co Deartet of Matheatcs
More informationResearch Article Multidimensional Hilbert-Type Inequalities with a Homogeneous Kernel
Hdaw Publshg Corporato Joural of Iequaltes ad Applcatos Volume 29, Artcle ID 3958, 2 pages do:.55/29/3958 Research Artcle Multdmesoal Hlbert-Type Iequaltes wth a Homogeeous Kerel Predrag Vuovć Faculty
More informationNon-uniform Turán-type problems
Joural of Combatoral Theory, Seres A 111 2005 106 110 wwwelsevercomlocatecta No-uform Turá-type problems DhruvMubay 1, Y Zhao 2 Departmet of Mathematcs, Statstcs, ad Computer Scece, Uversty of Illos at
More informationJournal of Mathematical Analysis and Applications
J. Math. Aal. Appl. 365 200) 358 362 Cotets lsts avalable at SceceDrect Joural of Mathematcal Aalyss ad Applcatos www.elsever.com/locate/maa Asymptotc behavor of termedate pots the dfferetal mea value
More informationMarcinkiewicz strong laws for linear statistics of ρ -mixing sequences of random variables
Aas da Academa Braslera de Cêcas 2006 784: 65-62 Aals of the Brazla Academy of Sceces ISSN 000-3765 www.scelo.br/aabc Marckewcz strog laws for lear statstcs of ρ -mxg sequeces of radom varables GUANG-HUI
More informationSome Different Perspectives on Linear Least Squares
Soe Dfferet Perspectves o Lear Least Squares A stadard proble statstcs s to easure a respose or depedet varable, y, at fed values of oe or ore depedet varables. Soetes there ests a deterstc odel y f (,,
More informationA Remark on the Uniform Convergence of Some Sequences of Functions
Advaces Pure Mathematcs 05 5 57-533 Publshed Ole July 05 ScRes. http://www.scrp.org/joural/apm http://dx.do.org/0.436/apm.05.59048 A Remark o the Uform Covergece of Some Sequeces of Fuctos Guy Degla Isttut
More informationEntropy ISSN by MDPI
Etropy 2003, 5, 233-238 Etropy ISSN 1099-4300 2003 by MDPI www.mdp.org/etropy O the Measure Etropy of Addtve Cellular Automata Hasa Aı Arts ad Sceces Faculty, Departmet of Mathematcs, Harra Uversty; 63100,
More informationThe Mathematical Appendix
The Mathematcal Appedx Defto A: If ( Λ, Ω, where ( λ λ λ whch the probablty dstrbutos,,..., Defto A. uppose that ( Λ,,..., s a expermet type, the σ-algebra o λ λ λ are defed s deoted by ( (,,...,, σ Ω.
More informationSome identities involving the partial sum of q-binomial coefficients
Some dettes volvg the partal sum of -bomal coeffcets Bg He Departmet of Mathematcs, Shagha Key Laboratory of PMMP East Cha Normal Uversty 500 Dogchua Road, Shagha 20024, People s Republc of Cha yuhe00@foxmal.com
More informationON WEIGHTED INTEGRAL AND DISCRETE OPIAL TYPE INEQUALITIES
M atheatcal I equaltes & A pplcatos Volue 19, Nuber 4 16, 195 137 do:1.7153/a-19-95 ON WEIGHTED INTEGRAL AND DISCRETE OPIAL TYPE INEQUALITIES MAJA ANDRIĆ, JOSIP PEČARIĆ AND IVAN PERIĆ Coucated by C. P.
More informationA Characterization of Jacobson Radical in Γ-Banach Algebras
Advaces Pure Matheatcs 43-48 http://dxdoorg/436/ap66 Publshed Ole Noveber (http://wwwscrporg/joural/ap) A Characterzato of Jacobso Radcal Γ-Baach Algebras Nlash Goswa Departet of Matheatcs Gauhat Uversty
More informationA Study on Generalized Generalized Quasi hyperbolic Kac Moody algebra QHGGH of rank 10
Global Joural of Mathematcal Sceces: Theory ad Practcal. ISSN 974-3 Volume 9, Number 3 (7), pp. 43-4 Iteratoal Research Publcato House http://www.rphouse.com A Study o Geeralzed Geeralzed Quas (9) hyperbolc
More informationASYMPTOTIC STABILITY OF TIME VARYING DELAY-DIFFERENCE SYSTEM VIA MATRIX INEQUALITIES AND APPLICATION
Joural of the Appled Matheatcs Statstcs ad Iforatcs (JAMSI) 6 (00) No. ASYMPOIC SABILIY OF IME VARYING DELAY-DIFFERENCE SYSEM VIA MARIX INEQUALIIES AND APPLICAION KREANGKRI RACHAGI Abstract I ths paper
More informationMULTIOBJECTIVE NONLINEAR FRACTIONAL PROGRAMMING PROBLEMS INVOLVING GENERALIZED d - TYPE-I n -SET FUNCTIONS
THE PUBLIHING HOUE PROCEEDING OF THE ROMANIAN ACADEMY, eres A OF THE ROMANIAN ACADEMY Volue 8, Nuber /27,.- MULTIOBJECTIVE NONLINEAR FRACTIONAL PROGRAMMING PROBLEM INVOLVING GENERALIZED d - TYPE-I -ET
More informationˆn i 1 ni ni Ž. Ý Ý CENTRAL LIMIT THEOREM FOR LINEAR PROCESSES
The Aals of Proalty 997, Vol. 5, No., 443456 CENTRAL LIMIT THEOREM FOR LINEAR PROCESSES BY MAGDA PELIGRAD AND SERGEY UTEV Uversty of Ccat ad Isttute of MathematcsNovosrs I ths paper we study the CLT for
More informationSTRONG CONSISTENCY OF LEAST SQUARES ESTIMATE IN MULTIPLE REGRESSION WHEN THE ERROR VARIANCE IS INFINITE
Statstca Sca 9(1999), 289-296 STRONG CONSISTENCY OF LEAST SQUARES ESTIMATE IN MULTIPLE REGRESSION WHEN THE ERROR VARIANCE IS INFINITE J Mgzhog ad Che Xru GuZhou Natoal College ad Graduate School, Chese
More informationON THE LOGARITHMIC INTEGRAL
Hacettepe Joural of Mathematcs ad Statstcs Volume 39(3) (21), 393 41 ON THE LOGARITHMIC INTEGRAL Bra Fsher ad Bljaa Jolevska-Tueska Receved 29:9 :29 : Accepted 2 :3 :21 Abstract The logarthmc tegral l(x)
More informationfor each of its columns. A quick calculation will verify that: thus m < dim(v). Then a basis of V with respect to which T has the form: A
Desty of dagoalzable square atrces Studet: Dael Cervoe; Metor: Saravaa Thyagaraa Uversty of Chcago VIGRE REU, Suer 7. For ths etre aer, we wll refer to V as a vector sace over ad L(V) as the set of lear
More informationarxiv: v4 [math.nt] 14 Aug 2015
arxv:52.799v4 [math.nt] 4 Aug 25 O the propertes of terated bomal trasforms for the Padova ad Perr matrx sequeces Nazmye Ylmaz ad Necat Tasara Departmet of Mathematcs, Faculty of Scece, Selcu Uversty,
More informationA New Method for Solving Fuzzy Linear. Programming by Solving Linear Programming
ppled Matheatcal Sceces Vol 008 o 50 7-80 New Method for Solvg Fuzzy Lear Prograg by Solvg Lear Prograg S H Nasser a Departet of Matheatcs Faculty of Basc Sceces Mazadara Uversty Babolsar Ira b The Research
More informationρ < 1 be five real numbers. The
Lecture o BST 63: Statstcal Theory I Ku Zhag, /0/006 Revew for the prevous lecture Deftos: covarace, correlato Examples: How to calculate covarace ad correlato Theorems: propertes of correlato ad covarace
More informationChapter 4 Multiple Random Variables
Revew for the prevous lecture: Theorems ad Examples: How to obta the pmf (pdf) of U = g (, Y) ad V = g (, Y) Chapter 4 Multple Radom Varables Chapter 44 Herarchcal Models ad Mxture Dstrbutos Examples:
More informationA CHARACTERIZATION OF THE CLIFFORD TORUS
PROCEEDINGS OF THE AERICAN ATHEATICAL SOCIETY Volue 17, Nuber 3, arch 1999, Pages 819 88 S 000-9939(99)05088-1 A CHARACTERIZATION OF THE CLIFFORD TORUS QING-ING CHENG AND SUSUU ISHIKAWA (Coucated by Chrstopher
More informationA tighter lower bound on the circuit size of the hardest Boolean functions
Electroc Colloquum o Computatoal Complexty, Report No. 86 2011) A tghter lower boud o the crcut sze of the hardest Boolea fuctos Masak Yamamoto Abstract I [IPL2005], Fradse ad Mlterse mproved bouds o the
More informationAbstract. 1. Introduction
Joura of Mathematca Sceces: Advaces ad Appcatos Voume 4 umber 2 2 Pages 33-34 COVERGECE OF HE PROJECO YPE SHKAWA ERAO PROCESS WH ERRORS FOR A FE FAMY OF OSEF -ASYMPOCAY QUAS-OEXPASVE MAPPGS HUA QU ad S-SHEG
More informationOn L- Fuzzy Sets. T. Rama Rao, Ch. Prabhakara Rao, Dawit Solomon And Derso Abeje.
Iteratoal Joural of Fuzzy Mathematcs ad Systems. ISSN 2248-9940 Volume 3, Number 5 (2013), pp. 375-379 Research Ida Publcatos http://www.rpublcato.com O L- Fuzzy Sets T. Rama Rao, Ch. Prabhakara Rao, Dawt
More informationTHE TRUNCATED RANDIĆ-TYPE INDICES
Kragujeac J Sc 3 (00 47-5 UDC 547:54 THE TUNCATED ANDIĆ-TYPE INDICES odjtaba horba, a ohaad Al Hossezadeh, b Ia uta c a Departet of atheatcs, Faculty of Scece, Shahd ajae Teacher Trag Uersty, Tehra, 785-3,
More informationExtreme Value Theory: An Introduction
(correcto d Extreme Value Theory: A Itroducto by Laures de Haa ad Aa Ferrera Wth ths webpage the authors ted to form the readers of errors or mstakes foud the book after publcato. We also gve extesos for
More informationParameter, Statistic and Random Samples
Parameter, Statstc ad Radom Samples A parameter s a umber that descrbes the populato. It s a fxed umber, but practce we do ot kow ts value. A statstc s a fucto of the sample data,.e., t s a quatty whose
More informationExchangeable Sequences, Laws of Large Numbers, and the Mortgage Crisis.
Exchageable Sequeces, Laws of Large Numbers, ad the Mortgage Crss. Myug Joo Sog Advsor: Prof. Ja Madel May 2009 Itroducto The law of large umbers for..d. sequece gves covergece of sample meas to a costat,.e.,
More informationA Note on the Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Partial Sums of Certain Stationary Gaussian Sequences *
Appe Matheatcs 0 5 598-608 Pubshe Oe Jue 0 ScRes http://wwwscrporg/joura/a http://xoorg/06/a0505 A Note o the Aost Sure Cetra Lt Theore the Jot Verso for the Maxa a Parta Sus of Certa Statoary Gaussa Sequeces
More informationMahmud Masri. When X is a Banach algebra we show that the multipliers M ( L (,
O Multlers of Orlcz Saces حول مضاعفات فضاءات ا ورلكس Mahmud Masr Mathematcs Deartmet,. A-Najah Natoal Uversty, Nablus, Paleste Receved: (9/10/000), Acceted: (7/5/001) Abstract Let (, M, ) be a fte ostve
More informationInternational Journal of Mathematical Archive-5(8), 2014, Available online through ISSN
Iteratoal Joural of Mathematcal Archve-5(8) 204 25-29 Avalable ole through www.jma.fo ISSN 2229 5046 COMMON FIXED POINT OF GENERALIZED CONTRACTION MAPPING IN FUZZY METRIC SPACES Hamd Mottagh Golsha* ad
More informationarxiv:math/ v1 [math.gm] 8 Dec 2005
arxv:math/05272v [math.gm] 8 Dec 2005 A GENERALIZATION OF AN INEQUALITY FROM IMO 2005 NIKOLAI NIKOLOV The preset paper was spred by the thrd problem from the IMO 2005. A specal award was gve to Yure Boreko
More informationRelations to Other Statistical Methods Statistical Data Analysis with Positive Definite Kernels
Relatos to Other Statstcal Methods Statstcal Data Aalyss wth Postve Defte Kerels Kej Fukuzu Isttute of Statstcal Matheatcs, ROIS Departet of Statstcal Scece, Graduate Uversty for Advaced Studes October
More informationInterval extension of Bézier curve
WSEAS TRANSACTIONS o SIGNAL ROCESSING Jucheg L Iterval exteso of Bézer curve JUNCHENG LI Departet of Matheatcs Hua Uversty of Huates Scece ad Techology Dxg Road Loud cty Hua rovce 47 R CHINA E-al: ljucheg8@6co
More informationBounds for the Connective Eccentric Index
It. J. Cotemp. Math. Sceces, Vol. 7, 0, o. 44, 6-66 Bouds for the Coectve Eccetrc Idex Nlaja De Departmet of Basc Scece, Humates ad Socal Scece (Mathematcs Calcutta Isttute of Egeerg ad Maagemet Kolkata,
More informationSome results and conjectures about recurrence relations for certain sequences of binomial sums.
Soe results ad coectures about recurrece relatos for certa sequeces of boal sus Joha Cgler Faultät für Matheat Uverstät We A-9 We Nordbergstraße 5 Joha Cgler@uveacat Abstract I a prevous paper [] I have
More informationResearch Article Gauss-Lobatto Formulae and Extremal Problems
Hdaw Publshg Corporato Joural of Iequaltes ad Applcatos Volume 2008 Artcle ID 624989 0 pages do:055/2008/624989 Research Artcle Gauss-Lobatto Formulae ad Extremal Problems wth Polyomals Aa Mara Acu ad
More informationSebastián Martín Ruiz. Applications of Smarandache Function, and Prime and Coprime Functions
Sebastá Martí Ruz Alcatos of Saradache Fucto ad Pre ad Core Fuctos 0 C L f L otherwse are core ubers Aerca Research Press Rehoboth 00 Sebastá Martí Ruz Avda. De Regla 43 Choa 550 Cadz Sa Sarada@telele.es
More informationMAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES
Commu Korea Math Soc 26 20, No, pp 5 6 DOI 0434/CKMS20265 MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES Wag Xueju, Hu Shuhe, Li Xiaoqi, ad Yag Wezhi Abstract Let {X, } be a sequece
More informationArithmetic Mean and Geometric Mean
Acta Mathematca Ntresa Vol, No, p 43 48 ISSN 453-6083 Arthmetc Mea ad Geometrc Mea Mare Varga a * Peter Mchalča b a Departmet of Mathematcs, Faculty of Natural Sceces, Costate the Phlosopher Uversty Ntra,
More information9 U-STATISTICS. Eh =(m!) 1 Eh(X (1),..., X (m ) ) i.i.d
9 U-STATISTICS Suppose,,..., are P P..d. wth CDF F. Our goal s to estmate the expectato t (P)=Eh(,,..., m ). Note that ths expectato requres more tha oe cotrast to E, E, or Eh( ). Oe example s E or P((,
More informationSummary of the lecture in Biostatistics
Summary of the lecture Bostatstcs Probablty Desty Fucto For a cotuos radom varable, a probablty desty fucto s a fucto such that: 0 dx a b) b a dx A probablty desty fucto provdes a smple descrpto of the
More informationLecture 3 Probability review (cont d)
STATS 00: Itroducto to Statstcal Iferece Autum 06 Lecture 3 Probablty revew (cot d) 3. Jot dstrbutos If radom varables X,..., X k are depedet, the ther dstrbuto may be specfed by specfyg the dvdual dstrbuto
More informationIntroduction to Probability
Itroducto to Probablty Nader H Bshouty Departmet of Computer Scece Techo 32000 Israel e-mal: bshouty@cstechoacl 1 Combatorcs 11 Smple Rules I Combatorcs The rule of sum says that the umber of ways to choose
More informationStandard Deviation for PDG Mass Data
4 Dec 06 Stadard Devato for PDG Mass Data M. J. Gerusa Retred, 47 Clfde Road, Worghall, HP8 9JR, UK. gerusa@aol.co, phoe: +(44) 844 339754 Abstract Ths paper aalyses the data for the asses of eleetary
More informationFunctions of Random Variables
Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,
More informationLecture 4 Sep 9, 2015
CS 388R: Radomzed Algorthms Fall 205 Prof. Erc Prce Lecture 4 Sep 9, 205 Scrbe: Xagru Huag & Chad Voegele Overvew I prevous lectures, we troduced some basc probablty, the Cheroff boud, the coupo collector
More information1 Onto functions and bijections Applications to Counting
1 Oto fuctos ad bectos Applcatos to Coutg Now we move o to a ew topc. Defto 1.1 (Surecto. A fucto f : A B s sad to be surectve or oto f for each b B there s some a A so that f(a B. What are examples of
More information,m = 1,...,n; 2 ; p m (1 p) n m,m = 0,...,n; E[X] = np; n! e λ,n 0; E[X] = λ.
CS70: Lecture 21. Revew: Dstrbutos Revew: Idepedece Varace; Iequaltes; WLLN 1. Revew: Dstrbutos 2. Revew: Idepedece 3. Varace 4. Iequaltes Markov Chebyshev 5. Weak Law of Large Numbers U[1,...,] : Pr[X
More informationThe Primitive Idempotents in
Iteratoal Joural of Algebra, Vol, 00, o 5, 3 - The Prmtve Idempotets FC - I Kulvr gh Departmet of Mathematcs, H College r Jwa Nagar (rsa)-5075, Ida kulvrsheora@yahoocom K Arora Departmet of Mathematcs,
More informationGeneralized Convex Functions on Fractal Sets and Two Related Inequalities
Geeralzed Covex Fuctos o Fractal Sets ad Two Related Iequaltes Huxa Mo, X Su ad Dogya Yu 3,,3School of Scece, Bejg Uversty of Posts ad Telecommucatos, Bejg,00876, Cha, Correspodece should be addressed
More information18.413: Error Correcting Codes Lab March 2, Lecture 8
18.413: Error Correctg Codes Lab March 2, 2004 Lecturer: Dael A. Spelma Lecture 8 8.1 Vector Spaces A set C {0, 1} s a vector space f for x all C ad y C, x + y C, where we take addto to be compoet wse
More informationThe Occupancy and Coupon Collector problems
Chapter 4 The Occupacy ad Coupo Collector problems By Sarel Har-Peled, Jauary 9, 08 4 Prelmares [ Defto 4 Varace ad Stadard Devato For a radom varable X, let V E [ X [ µ X deote the varace of X, where
More informationV. Hemalatha, V. Mohana Selvi,
Iteratoal Joural of Scetfc & Egeerg Research, Volue 6, Issue, Noveber-0 ISSN - SUPER GEOMETRIC MEAN LABELING OF SOME CYCLE RELATED GRAPHS V Healatha, V Mohaa Selv, ABSTRACT-Let G be a graph wth p vertces
More informationProbabilistic Meanings of Numerical Characteristics for Single Birth Processes
A^VÇÚO 32 ò 5 Ï 206 c 0 Chese Joural of Appled Probablty ad Statstcs Oct 206 Vol 32 No 5 pp 452-462 do: 03969/jss00-426820605002 Probablstc Meags of Numercal Characterstcs for Sgle Brth Processes LIAO
More informationOn Submanifolds of an Almost r-paracontact Riemannian Manifold Endowed with a Quarter Symmetric Metric Connection
Theoretcal Mathematcs & Applcatos vol. 4 o. 4 04-7 ISS: 79-9687 prt 79-9709 ole Scepress Ltd 04 O Submafolds of a Almost r-paracotact emaa Mafold Edowed wth a Quarter Symmetrc Metrc Coecto Mob Ahmad Abdullah.
More informationA Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions
Appled Matheatcs, 1, 4, 8-88 http://d.do.org/1.4/a.1.448 Publshed Ole Aprl 1 (http://www.scrp.org/joural/a) A Covetoal Approach for the Soluto of the Ffth Order Boudary Value Probles Usg Sth Degree Sple
More information3.1 Introduction to Multinomial Logit and Probit
ES3008 Ecooetrcs Lecture 3 robt ad Logt - Multoal 3. Itroducto to Multoal Logt ad robt 3. Estato of β 3. Itroducto to Multoal Logt ad robt The ultoal Logt odel s used whe there are several optos (ad therefore
More informationLower Bounds of the Kirchhoff and Degree Kirchhoff Indices
SCIENTIFIC PUBLICATIONS OF THE STATE UNIVERSITY OF NOVI PAZAR SER. A: APPL. MATH. INFORM. AND MECH. vol. 7, (205), 25-3. Lower Bouds of the Krchhoff ad Degree Krchhoff Idces I. Ž. Mlovaovć, E. I. Mlovaovć,
More informationOn the construction of symmetric nonnegative matrix with prescribed Ritz values
Joural of Lear ad Topologcal Algebra Vol. 3, No., 14, 61-66 O the costructo of symmetrc oegatve matrx wth prescrbed Rtz values A. M. Nazar a, E. Afshar b a Departmet of Mathematcs, Arak Uversty, P.O. Box
More informationAitken delta-squared generalized Juncgk-type iterative procedure
Atke delta-squared geeralzed Jucgk-type teratve procedure M. De la Se Isttute of Research ad Developmet of Processes. Uversty of Basque Coutry Campus of Leoa (Bzkaa) PO Box. 644- Blbao, 488- Blbao. SPAIN
More informationUniform asymptotical stability of almost periodic solution of a discrete multispecies Lotka-Volterra competition system
Iteratoal Joural of Egeerg ad Advaced Research Techology (IJEART) ISSN: 2454-9290, Volume-2, Issue-1, Jauary 2016 Uform asymptotcal stablty of almost perodc soluto of a dscrete multspeces Lotka-Volterra
More informationOPTIMALITY CONDITIONS FOR LOCALLY LIPSCHITZ GENERALIZED B-VEX SEMI-INFINITE PROGRAMMING
Mrcea cel Batra Naval Acadey Scetfc Bullet, Volue XIX 6 Issue he joural s dexed : PROQUES / DOAJ / Crossref / EBSCOhost / INDEX COPERNICUS / DRJI / OAJI / JOURNAL INDEX / IOR / SCIENCE LIBRARY INDEX /
More informationCorrelation of Neutrosophic Sets in Probability Spaces
JMSI 10 014 No. 1 45 orrelato of Neutrosophc Sets Probablty Spaces I.M. HNFY.. SLM O. M. KHLED ND K. M. MHFOUZ bstract I ths paper we troduce ad study the cocepts of correlato ad correlato coeffcet of
More informationThe Number of the Two Dimensional Run Length Constrained Arrays
2009 Iteratoal Coferece o Mache Learg ad Coutg IPCSIT vol.3 (20) (20) IACSIT Press Sgaore The Nuber of the Two Desoal Ru Legth Costraed Arrays Tal Ataa Naohsa Otsua 2 Xuerog Yog 3 School of Scece ad Egeerg
More informationAsymptotic Behavior of Solutions of Nonlinear Delay Differential Equations With Impulse
P a g e Vol Issue7Ver,oveber Global Joural of Scece Froer Research Asypoc Behavor of Soluos of olear Delay Dffereal Equaos Wh Ipulse Zhag xog GJSFR Classfcao - F FOR 3 Absrac Ths paper sudes he asypoc
More informationarxiv: v1 [math.st] 24 Oct 2016
arxv:60.07554v [math.st] 24 Oct 206 Some Relatoshps ad Propertes of the Hypergeometrc Dstrbuto Peter H. Pesku, Departmet of Mathematcs ad Statstcs York Uversty, Toroto, Otaro M3J P3, Caada E-mal: pesku@pascal.math.yorku.ca
More informationSimulation Output Analysis
Smulato Output Aalyss Summary Examples Parameter Estmato Sample Mea ad Varace Pot ad Iterval Estmato ermatg ad o-ermatg Smulato Mea Square Errors Example: Sgle Server Queueg System x(t) S 4 S 4 S 3 S 5
More information#A27 INTEGERS 13 (2013) SOME WEIGHTED SUMS OF PRODUCTS OF LUCAS SEQUENCES
#A27 INTEGERS 3 (203) SOME WEIGHTED SUMS OF PRODUCTS OF LUCAS SEQUENCES Emrah Kılıç Mathematcs Departmet, TOBB Uversty of Ecoomcs ad Techology, Akara, Turkey eklc@etu.edu.tr Neşe Ömür Mathematcs Departmet,
More informationh-analogue of Fibonacci Numbers
h-aalogue of Fboacc Numbers arxv:090.0038v [math-ph 30 Sep 009 H.B. Beaoum Prce Mohammad Uversty, Al-Khobar 395, Saud Araba Abstract I ths paper, we troduce the h-aalogue of Fboacc umbers for o-commutatve
More informationA New Method for Decision Making Based on Soft Matrix Theory
Joural of Scetfc esearch & eports 3(5): 0-7, 04; rtcle o. JS.04.5.00 SCIENCEDOMIN teratoal www.scecedoma.org New Method for Decso Mag Based o Soft Matrx Theory Zhmg Zhag * College of Mathematcs ad Computer
More information= y and Normed Linear Spaces
304-50 LINER SYSTEMS Lectue 8: Solutos to = ad Nomed Lea Spaces 73 Fdg N To fd N, we eed to chaacteze all solutos to = 0 Recall that ow opeatos peseve N, so that = 0 = 0 We ca solve = 0 ecusvel backwads
More informationAbout k-perfect numbers
DOI: 0.47/auom-04-0005 A. Şt. Uv. Ovdus Costaţa Vol.,04, 45 50 About k-perfect umbers Mhály Becze Abstract ABSTRACT. I ths paper we preset some results about k-perfect umbers, ad geeralze two equaltes
More information1 Lyapunov Stability Theory
Lyapuov Stablty heory I ths secto we cosder proofs of stablty of equlbra of autoomous systems. hs s stadard theory for olear systems, ad oe of the most mportat tools the aalyss of olear systems. It may
More information