saqatvelos eceebata eovl aaes oabe # 9 BUETIN OF THE GEORGIAN NATIONA AADEM OF SIENES vol o 9 Maheacs O Oe Pope o he Wee Ieal a s Sascal Applcao Pee Babla* Elzba Naaaa** Mzeva Pasasa & Gol Sohaze # * I Javahshvl Tbls Sae Uves ** Acae Mebe I Javahshvl Tbls Sae Uves & Soh Uves # A Tseeel Sae Uves as ABSTRAT Fo he Wee eal oe pope o veso s esablshe Ths pope s se o cosco o opaaec sascal esao o he o loahc evave o sbo ao pocesses hch s obseve Wee ose 9 Bll Geo Nal Aca Sc e os: Wee eal loahc evave opaaec esao e he s o epee ao pocesses ξ η hee s a saa Wee pocess be e obsevao Us he obseve vales (aecoes ξ ξ ξ e ae o cosc a esae o he o loahc evave o he sbo o he pocess η Fo ao vales (he η a o o epe o hs poble s cosee [] he oe-esoal case To solve he poble e appl he echqe o opaaec esao o Wee eals I he s pa o hs o e ve oe veso heoe o he Wee eal Ths heoe eealzes he ell-o esl o Rooe [] o he oe-esoal case I he Wee eal heo hs esl s o epee ees a eables s o cosc he seco pa o he o e-esoal appoaos o esao o he o loahc evave e-esoal space We ll cose he space o coos cos o [ ] he -aleba o Boel sbses a he Wee ease μ o e he ( a be pos o [ ] We ll eoe b ( he F be soe coal o I s asse ha boe le h veces a he pos ( ( ( F ( F ( ( e I s esoo ha o e have F ( F he sese o so coveece I s ell o ([] ha o a coos boe coal F ebese eal h espec o a Wee ease ( s hs eal ha s calle he Wee eal ca be ee b he eqal F μ ( l π 9 Bll Geo Nal Aca Sc
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O Oe Pope o he Wee Ieal a s Sascal Applcao 9 So he ollo saee s e Theoe I he space [ ] e have he obsevao o he ealzao o he s o epee ao pocesses W hee W s a saa Wee pocess he he esae o he loahc evave o he sbo o he ao pocess s ve b he ola l D a ( ( hϕ( l ( h l l D ϕ hee ( ( s a eve posve sooh es co < < [ ] a as ae chose so ha < as he pos ateaa ves eals et Tvsebsa a s sas aoeebs Sesaeb pee babla* elzba aaaa** zeva acaca & ol soaze # * avasvls sa Tblss saelo vese ** aaes ev avasvls sa Tblss saelo vese & sos vese # a eetls saelo vese qtas asos aela ves eals Sebebs et Tvseba oelc aoeeba cob loatl aoebls aapaael sas Seasebs asaeba set SeTvevT pocess aalebsatvs oelzec avveba eba ves SeSoTebs pobebs REFERENES E Naaaa (989 Nopaaec esao o pobabl eses a eesso cves le Acaec Pblshes Gop Doech P Rooe (957 aa J Mah 9: 5- I M ovalch (96 UMN (Avaces o Maheacal Sceces VIII (9: 97- ( Rssa Dales (967 UMN (Avaces o Maheacal Sceces : -5 ( Rssa Receve Decebe 8 Bll Geo Nal Aca Sc vol o 9