Large Deviations Techniques and Applications
|
|
- Angelica Banks
- 5 years ago
- Views:
Transcription
1 Amir Dembo Ofer Zeitouni Large Deviations Techniques and Applications Second Edition With 29 Figures Springer
2 Contents Preface to the Second Edition Preface to the First Edition vii ix 1 Introduction Rare Events and Large Deviations The Large Deviation Principle Historical Notes and References 9 2 LDP for Finite Dimensional Spaces Combinatorial Techniques for Finite Alphabets The Method of Types and Sanov's Theorem Cramer's Theorem for Finite Alphabets in IR Large Deviations for Sampling Without Replacement Cramer's Theorem Cramer's Theorem in IR Cramer's Theorem in M d The Gartner-Ellis Theorem Concentration Inequalities Inequalities for Bounded Martingale Differences Talagrand's Concentration Inequalities Historical Notes and References 68 xin
3 xiv 3 Applications The Finite Dimensional Case Large Deviations for Finite State Markov Chains LDP for Additive Functionals of Markov Chains Sanov's Theorem for the Empirical Measure of Markov Chains Sanov's Theorem for the Pair Empirical Measure of Markov Chains Long Rare Segments in Random Walks The Gibbs Conditioning Principle for Finite Alphabets The Hypothesis Testing Problem Generalized Likelihood Ratio Test for Finite Alphabets Rate Distortion Theory Moderate Deviations and Exact Asymptotics in IR d Historical Notes and References General Principles Existence of an LDP and Related Properties Properties of the LDP The Existence of an LDP Transformations of LDPs Contraction Principles Exponential Approximations Varadhan's Integral Lemma Bryc's Inverse Varadhan Lemma LDP in Topological Vector Spaces A General Upper Bound Convexity Considerations Abstract Gartner-Ellis Theorem Large Deviations for Projective Limits The LDP and Weak Convergence in Metric Spaces Historical Notes and References.. 173
4 XV 5 Sample Path Large Deviations Sample Path Large Deviations for Random Walks Brownian Motion Sample Path Large Deviations Multivariate Random Walk and Brownian Sheet Performance Analysis of DMPSK Modulation Large Exceedances in IR d The Freidlin-Wentzell Theory The Problem of Diffusion Exit from a Domain The Performance of Tracking Loops An Angular Tracking Loop Analysis The Analysis of Range Tracking Loops Historical Notes and References The LDP for Abstract Empirical Measures Cramer's Theorem in Polish Spaces Sanov's Theorem LDP for the Empirical Measure The Uniform Markov Case Mixing Conditions and LDP LDP for the Empirical Mean in K d Empirical Measure LDP for Mixing Processes LDP for Empirical Measures of Markov Chains LDP for Occupation Times LDP for the fc-empirical Measures Process Level LDP for Markov Chains A Weak Convergence Approach to Large Deviations Historical Notes and References. ^ Applications of Empirical Measures LDP Universal Hypothesis Testing A General Statement of Test Optimality Independent and Identically Distributed Observations Sampling Without Replacement 318
5 xvi 7.3 The Gibbs Conditioning Principle The Non-Interacting Case The Interacting Case Refinements of the Gibbs Conditioning Principle Historical Notes and References 338 Appendix 341 A Convex Analysis Considerations in lr d 341 B Topological Preliminaries 343 B.I Generalities 343 B.2 Topological Vector Spaces and Weak Topologies B.3 Banach and Polish Spaces 347 B.4 Mazur's Theorem 349 C Integration and Function Spaces 350 C.I Additive Set Functions 350 C.2 Integration and Spaces of Functions 352 D Probability Measures on Polish Spaces 354 D.I Generalities 354 D.2 Weak Topology 355 D.3 Product Space and Relative Entropy Decompositions 357 E Stochastic Analysis 359 Bibliography 363 General Conventions 385 Index of Notation 387 Index 391
COPYRIGHTED MATERIAL CONTENTS. Preface Preface to the First Edition
Preface Preface to the First Edition xi xiii 1 Basic Probability Theory 1 1.1 Introduction 1 1.2 Sample Spaces and Events 3 1.3 The Axioms of Probability 7 1.4 Finite Sample Spaces and Combinatorics 15
More informationProbability via Expectation
Peter Whittle Probability via Expectation Fourth Edition With 22 Illustrations Springer Contents Preface to the Fourth Edition Preface to the Third Edition Preface to the Russian Edition of Probability
More informationLarge deviation convergence of generated pseudo measures
Large deviation convergence of generated pseudo measures Ljubo Nedović 1, Endre Pap 2, Nebojša M. Ralević 1, Tatjana Grbić 1 1 Faculty of Engineering, University of Novi Sad Trg Dositeja Obradovića 6,
More informationAn Introduction to Probability Theory and Its Applications
An Introduction to Probability Theory and Its Applications WILLIAM FELLER (1906-1970) Eugene Higgins Professor of Mathematics Princeton University VOLUME II SECOND EDITION JOHN WILEY & SONS Contents I
More informationProbability for Statistics and Machine Learning
~Springer Anirban DasGupta Probability for Statistics and Machine Learning Fundamentals and Advanced Topics Contents Suggested Courses with Diffe~ent Themes........................... xix 1 Review of Univariate
More informationELEMENTS O F INFORMATION THEORY
ELEMENTS O F INFORMATION THEORY THOMAS M. COVER JOY A. THOMAS Preface to the Second Edition Preface to the First Edition Acknowledgments for the Second Edition Acknowledgments for the First Edition x
More informationNotes on Large Deviations in Economics and Finance. Noah Williams
Notes on Large Deviations in Economics and Finance Noah Williams Princeton University and NBER http://www.princeton.edu/ noahw Notes on Large Deviations 1 Introduction What is large deviation theory? Loosely:
More informationLarge-deviation theory and coverage in mobile phone networks
Weierstrass Institute for Applied Analysis and Stochastics Large-deviation theory and coverage in mobile phone networks Paul Keeler, Weierstrass Institute for Applied Analysis and Stochastics, Berlin joint
More informationStochastic Partial Differential Equations with Levy Noise
Stochastic Partial Differential Equations with Levy Noise An Evolution Equation Approach S..PESZAT and J. ZABCZYK Institute of Mathematics, Polish Academy of Sciences' CAMBRIDGE UNIVERSITY PRESS Contents
More informationA Note On Large Deviation Theory and Beyond
A Note On Large Deviation Theory and Beyond Jin Feng In this set of notes, we will develop and explain a whole mathematical theory which can be highly summarized through one simple observation ( ) lim
More informationTime Series: Theory and Methods
Peter J. Brockwell Richard A. Davis Time Series: Theory and Methods Second Edition With 124 Illustrations Springer Contents Preface to the Second Edition Preface to the First Edition vn ix CHAPTER 1 Stationary
More informationMonte Carlo Methods. Handbook of. University ofqueensland. Thomas Taimre. Zdravko I. Botev. Dirk P. Kroese. Universite de Montreal
Handbook of Monte Carlo Methods Dirk P. Kroese University ofqueensland Thomas Taimre University ofqueensland Zdravko I. Botev Universite de Montreal A JOHN WILEY & SONS, INC., PUBLICATION Preface Acknowledgments
More informationGärtner-Ellis Theorem and applications.
Gärtner-Ellis Theorem and applications. Elena Kosygina July 25, 208 In this lecture we turn to the non-i.i.d. case and discuss Gärtner-Ellis theorem. As an application, we study Curie-Weiss model with
More informationAn inverse of Sanov s theorem
An inverse of Sanov s theorem Ayalvadi Ganesh and Neil O Connell BRIMS, Hewlett-Packard Labs, Bristol Abstract Let X k be a sequence of iid random variables taking values in a finite set, and consider
More informationExtreme Value Theory An Introduction
Laurens de Haan Ana Ferreira Extreme Value Theory An Introduction fi Springer Contents Preface List of Abbreviations and Symbols vii xv Part I One-Dimensional Observations 1 Limit Distributions and Domains
More information2a Large deviation principle (LDP) b Contraction principle c Change of measure... 10
Tel Aviv University, 2007 Large deviations 5 2 Basic notions 2a Large deviation principle LDP......... 5 2b Contraction principle................ 9 2c Change of measure................. 10 The formalism
More informationElements of Multivariate Time Series Analysis
Gregory C. Reinsel Elements of Multivariate Time Series Analysis Second Edition With 14 Figures Springer Contents Preface to the Second Edition Preface to the First Edition vii ix 1. Vector Time Series
More informationSample path large deviations of a Gaussian process with stationary increments and regularily varying variance
Sample path large deviations of a Gaussian process with stationary increments and regularily varying variance Tommi Sottinen Department of Mathematics P. O. Box 4 FIN-0004 University of Helsinki Finland
More informationLarge Deviations for Weakly Dependent Sequences: The Gärtner-Ellis Theorem
Chapter 34 Large Deviations for Weakly Dependent Sequences: The Gärtner-Ellis Theorem This chapter proves the Gärtner-Ellis theorem, establishing an LDP for not-too-dependent processes taking values in
More informationLessons in Estimation Theory for Signal Processing, Communications, and Control
Lessons in Estimation Theory for Signal Processing, Communications, and Control Jerry M. Mendel Department of Electrical Engineering University of Southern California Los Angeles, California PRENTICE HALL
More information1. Principle of large deviations
1. Principle of large deviations This section will provide a short introduction to the Law of large deviations. The basic principle behind this theory centers on the observation that certain functions
More informationA Course on Large Deviations with an Introduction to Gibbs Measures. Firas Rassoul-Agha
A Course on Large Deviations with an Introduction to Gibbs Measures Firas Rassoul-Agha Timo Seppäläinen Department of Mathematics, University of Utah, 55 South 400 East, Salt Lake City, UT 842, USA E-mail
More informationBrownian intersection local times
Weierstrass Institute for Applied Analysis and Stochastics Brownian intersection local times Wolfgang König (TU Berlin and WIAS Berlin) [K.&M., Ann. Probab. 2002], [K.&M., Trans. Amer. Math. Soc. 2006]
More informationSTOCHASTIC PROCESSES IN PHYSICS AND CHEMISTRY
STOCHASTIC PROCESSES IN PHYSICS AND CHEMISTRY Third edition N.G. VAN KAMPEN Institute for Theoretical Physics of the University at Utrecht ELSEVIER Amsterdam Boston Heidelberg London New York Oxford Paris
More informationProbability and Stochastic Processes
Probability and Stochastic Processes A Friendly Introduction Electrical and Computer Engineers Third Edition Roy D. Yates Rutgers, The State University of New Jersey David J. Goodman New York University
More informationContents. 1 Preliminaries 3. Martingales
Table of Preface PART I THE FUNDAMENTAL PRINCIPLES page xv 1 Preliminaries 3 2 Martingales 9 2.1 Martingales and examples 9 2.2 Stopping times 12 2.3 The maximum inequality 13 2.4 Doob s inequality 14
More informationPART I INTRODUCTION The meaning of probability Basic definitions for frequentist statistics and Bayesian inference Bayesian inference Combinatorics
Table of Preface page xi PART I INTRODUCTION 1 1 The meaning of probability 3 1.1 Classical definition of probability 3 1.2 Statistical definition of probability 9 1.3 Bayesian understanding of probability
More informationFinding a Needle in a Haystack: Conditions for Reliable. Detection in the Presence of Clutter
Finding a eedle in a Haystack: Conditions for Reliable Detection in the Presence of Clutter Bruno Jedynak and Damianos Karakos October 23, 2006 Abstract We study conditions for the detection of an -length
More informationLarge deviation theory and applications
Large deviation theory and applications Peter Mörters November 0, 2008 Abstract Large deviation theory deals with the decay of the probability of increasingly unlikely events. It is one of the key techniques
More informationStochastic Models. Edited by D.P. Heyman Bellcore. MJ. Sobel State University of New York at Stony Brook
Stochastic Models Edited by D.P. Heyman Bellcore MJ. Sobel State University of New York at Stony Brook 1990 NORTH-HOLLAND AMSTERDAM NEW YORK OXFORD TOKYO Contents Preface CHARTER 1 Point Processes R.F.
More informationADAPTIVE FILTER THEORY
ADAPTIVE FILTER THEORY Fourth Edition Simon Haykin Communications Research Laboratory McMaster University Hamilton, Ontario, Canada Front ice Hall PRENTICE HALL Upper Saddle River, New Jersey 07458 Preface
More informationLarge deviations for weighted empirical measures and processes arising in importance sampling. Pierre Nyquist
Large deviations for weighted empirical measures and processes arising in importance sampling Pierre Nyquist Abstract This thesis consists of two papers related to large deviation results associated with
More informationH. DJELLOUT A. GUILLIN
ANNALES DE LA FACULTÉ DES SCIENCES DE TOULOUSE H. DJELLOUT A. GUILLIN Large and moderate deviations for moving average processes Annales de la faculté des sciences de Toulouse 6 e série, tome 10, n o 1
More informationIntroduction to Functional Analysis With Applications
Introduction to Functional Analysis With Applications A.H. Siddiqi Khalil Ahmad P. Manchanda Tunbridge Wells, UK Anamaya Publishers New Delhi Contents Preface vii List of Symbols.: ' - ix 1. Normed and
More informationElementary Applications of Probability Theory
Elementary Applications of Probability Theory With an introduction to stochastic differential equations Second edition Henry C. Tuckwell Senior Research Fellow Stochastic Analysis Group of the Centre for
More informationThéorie des grandes déviations: Des mathématiques à la physique
Théorie des grandes déviations: Des mathématiques à la physique Hugo Touchette National Institute for Theoretical Physics (NITheP) Stellenbosch, Afrique du Sud CERMICS, École des Ponts Paris, France 30
More informationFundamentals of Applied Probability and Random Processes
Fundamentals of Applied Probability and Random Processes,nd 2 na Edition Oliver C. Ibe University of Massachusetts, LoweLL, Massachusetts ip^ W >!^ AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS
More informationPRINCIPLES OF STATISTICAL INFERENCE
Advanced Series on Statistical Science & Applied Probability PRINCIPLES OF STATISTICAL INFERENCE from a Neo-Fisherian Perspective Luigi Pace Department of Statistics University ofudine, Italy Alessandra
More informationInformation Dynamics Foundations and Applications
Gustavo Deco Bernd Schürmann Information Dynamics Foundations and Applications With 89 Illustrations Springer PREFACE vii CHAPTER 1 Introduction 1 CHAPTER 2 Dynamical Systems: An Overview 7 2.1 Deterministic
More informationHANDBOOK OF APPLICABLE MATHEMATICS
HANDBOOK OF APPLICABLE MATHEMATICS Chief Editor: Walter Ledermann Volume VI: Statistics PART A Edited by Emlyn Lloyd University of Lancaster A Wiley-Interscience Publication JOHN WILEY & SONS Chichester
More informationAn Introduction to Stochastic Modeling
F An Introduction to Stochastic Modeling Fourth Edition Mark A. Pinsky Department of Mathematics Northwestern University Evanston, Illinois Samuel Karlin Department of Mathematics Stanford University Stanford,
More informationClasses of Linear Operators Vol. I
Classes of Linear Operators Vol. I Israel Gohberg Seymour Goldberg Marinus A. Kaashoek Birkhäuser Verlag Basel Boston Berlin TABLE OF CONTENTS VOLUME I Preface Table of Contents of Volume I Table of Contents
More informationStatistical Methods in HYDROLOGY CHARLES T. HAAN. The Iowa State University Press / Ames
Statistical Methods in HYDROLOGY CHARLES T. HAAN The Iowa State University Press / Ames Univariate BASIC Table of Contents PREFACE xiii ACKNOWLEDGEMENTS xv 1 INTRODUCTION 1 2 PROBABILITY AND PROBABILITY
More informationInfinite-Dimensional Dynamical Systems in Mechanics and Physics
Roger Temam Infinite-Dimensional Dynamical Systems in Mechanics and Physics Second Edition With 13 Illustrations Springer Contents Preface to the Second Edition Preface to the First Edition vii ix GENERAL
More informationGeneralized Neyman Pearson optimality of empirical likelihood for testing parameter hypotheses
Ann Inst Stat Math (2009) 61:773 787 DOI 10.1007/s10463-008-0172-6 Generalized Neyman Pearson optimality of empirical likelihood for testing parameter hypotheses Taisuke Otsu Received: 1 June 2007 / Revised:
More informationWeak convergence and large deviation theory
First Prev Next Go To Go Back Full Screen Close Quit 1 Weak convergence and large deviation theory Large deviation principle Convergence in distribution The Bryc-Varadhan theorem Tightness and Prohorov
More informationOXPORD UNIVERSITY PRESS
Concentration Inequalities A Nonasymptotic Theory of Independence STEPHANE BOUCHERON GABOR LUGOSI PASCAL MASS ART OXPORD UNIVERSITY PRESS CONTENTS 1 Introduction 1 1.1 Sums of Independent Random Variables
More informationContents. 2 Sequences and Series Approximation by Rational Numbers Sequences Basics on Sequences...
Contents 1 Real Numbers: The Basics... 1 1.1 Notation... 1 1.2 Natural Numbers... 4 1.3 Integers... 5 1.4 Fractions and Rational Numbers... 10 1.4.1 Introduction... 10 1.4.2 Powers and Radicals of Rational
More informationTesting Statistical Hypotheses
E.L. Lehmann Joseph P. Romano Testing Statistical Hypotheses Third Edition 4y Springer Preface vii I Small-Sample Theory 1 1 The General Decision Problem 3 1.1 Statistical Inference and Statistical Decisions
More informationHandbook of Stochastic Methods
C. W. Gardiner Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences Third Edition With 30 Figures Springer Contents 1. A Historical Introduction 1 1.1 Motivation I 1.2 Some Historical
More information1. Numerical Methods for Stochastic Control Problems in Continuous Time (with H. J. Kushner), Second Revised Edition, Springer-Verlag, New York, 2001.
Paul Dupuis Professor of Applied Mathematics Division of Applied Mathematics Brown University Publications Books: 1. Numerical Methods for Stochastic Control Problems in Continuous Time (with H. J. Kushner),
More informationIntroduction to. Process Control. Ahmet Palazoglu. Second Edition. Jose A. Romagnoli. CRC Press. Taylor & Francis Group. Taylor & Francis Group,
Introduction to Process Control Second Edition Jose A. Romagnoli Ahmet Palazoglu CRC Press Taylor & Francis Group Boca Raton London NewYork CRC Press is an imprint of the Taylor & Francis Group, an informa
More informationElliptic Partial Differential Equations of Second Order
David Gilbarg Neil S.Trudinger Elliptic Partial Differential Equations of Second Order Reprint of the 1998 Edition Springer Chapter 1. Introduction 1 Part I. Linear Equations Chapter 2. Laplace's Equation
More informationAdventures in Stochastic Processes
Sidney Resnick Adventures in Stochastic Processes with Illustrations Birkhäuser Boston Basel Berlin Table of Contents Preface ix CHAPTER 1. PRELIMINARIES: DISCRETE INDEX SETS AND/OR DISCRETE STATE SPACES
More informationQuantum Mechanics: Foundations and Applications
Arno Böhm Quantum Mechanics: Foundations and Applications Third Edition, Revised and Enlarged Prepared with Mark Loewe With 96 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo
More informationModules over Non-Noetherian Domains
Mathematical Surveys and Monographs Volume 84 Modules over Non-Noetherian Domains Laszlo Fuchs Luigi Sake American Mathematical Society Table of Contents Preface List of Symbols xi xv Chapter I. Commutative
More informationGROUP THEORY IN PHYSICS
GROUP THEORY IN PHYSICS Wu-Ki Tung World Scientific Philadelphia Singapore CONTENTS CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 PREFACE INTRODUCTION 1.1 Particle on a One-Dimensional Lattice 1.2 Representations
More informationPROBABILITY AND STOCHASTIC PROCESSES A Friendly Introduction for Electrical and Computer Engineers
PROBABILITY AND STOCHASTIC PROCESSES A Friendly Introduction for Electrical and Computer Engineers Roy D. Yates Rutgers, The State University ofnew Jersey David J. Goodman Rutgers, The State University
More informationThe large deviation principle for the Erdős-Rényi random graph
The large deviation principle for the Erdős-Rényi random graph (Courant Institute, NYU) joint work with S. R. S. Varadhan Main objective: how to count graphs with a given property Only consider finite
More informationDirectional Statistics
Directional Statistics Kanti V. Mardia University of Leeds, UK Peter E. Jupp University of St Andrews, UK I JOHN WILEY & SONS, LTD Chichester New York Weinheim Brisbane Singapore Toronto Contents Preface
More informationTesting Statistical Hypotheses
E.L. Lehmann Joseph P. Romano, 02LEu1 ttd ~Lt~S Testing Statistical Hypotheses Third Edition With 6 Illustrations ~Springer 2 The Probability Background 28 2.1 Probability and Measure 28 2.2 Integration.........
More informationEconometrica, Vol. 69, No. 6 (November, 2001), ASYMPTOTIC OPTIMALITY OF EMPIRICAL LIKELIHOOD FOR TESTING MOMENT RESTRICTIONS
Econometrica, Vol. 69, No. 6 (November, 200), 66 672 ASYMPTOTIC OPTIMALITY OF EMPIRICAL LIKELIHOOD FOR TESTING MOMENT RESTRICTIONS By Yuichi Kitamura introduction Economic theory often provides testable
More informationClassical Fourier Analysis
Loukas Grafakos Classical Fourier Analysis Second Edition 4y Springer 1 IP Spaces and Interpolation 1 1.1 V and Weak IP 1 1.1.1 The Distribution Function 2 1.1.2 Convergence in Measure 5 1.1.3 A First
More informationEntropy and Ergodic Theory Lecture 15: A first look at concentration
Entropy and Ergodic Theory Lecture 15: A first look at concentration 1 Introduction to concentration Let X 1, X 2,... be i.i.d. R-valued RVs with common distribution µ, and suppose for simplicity that
More informationIrr. Statistical Methods in Experimental Physics. 2nd Edition. Frederick James. World Scientific. CERN, Switzerland
Frederick James CERN, Switzerland Statistical Methods in Experimental Physics 2nd Edition r i Irr 1- r ri Ibn World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI CONTENTS
More informationMathematics for Economics and Finance
Mathematics for Economics and Finance Michael Harrison and Patrick Waldron B 375482 Routledge Taylor & Francis Croup LONDON AND NEW YORK Contents List of figures ix List of tables xi Foreword xiii Preface
More informationThe Bayesian Choice. Christian P. Robert. From Decision-Theoretic Foundations to Computational Implementation. Second Edition.
Christian P. Robert The Bayesian Choice From Decision-Theoretic Foundations to Computational Implementation Second Edition With 23 Illustrations ^Springer" Contents Preface to the Second Edition Preface
More informationMalvin H. Kalos, Paula A. Whitlock. Monte Carlo Methods. Second Revised and Enlarged Edition WILEY- BLACKWELL. WILEY-VCH Verlag GmbH & Co.
Malvin H. Kalos, Paula A. Whitlock Monte Carlo Methods Second Revised and Enlarged Edition WILEY- BLACKWELL WILEY-VCH Verlag GmbH & Co. KGaA v I Contents Preface to the Second Edition IX Preface to the
More informationINTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition
INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition Kerson Huang CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an Informa
More informationMATHEMATICS FOR ECONOMISTS. An Introductory Textbook. Third Edition. Malcolm Pemberton and Nicholas Rau. UNIVERSITY OF TORONTO PRESS Toronto Buffalo
MATHEMATICS FOR ECONOMISTS An Introductory Textbook Third Edition Malcolm Pemberton and Nicholas Rau UNIVERSITY OF TORONTO PRESS Toronto Buffalo Contents Preface Dependence of Chapters Answers and Solutions
More informationarxiv: v2 [math.pr] 30 Sep 2009
Upper and Lower Bounds in Exponential Tauberian Theorems Jochen Voss 3th September 9 arxiv:98.64v [math.pr] 3 Sep 9 Abstract In this text we study, for positive random variables, the relation between the
More informationGlobal Optimization, Generalized Canonical Ensembles, and Universal Ensemble Equivalence
Richard S. Ellis, Generalized Canonical Ensembles 1 Global Optimization, Generalized Canonical Ensembles, and Universal Ensemble Equivalence Richard S. Ellis Department of Mathematics and Statistics University
More informationSTAT 7032 Probability. Wlodek Bryc
STAT 7032 Probability Wlodek Bryc Revised for Spring 2019 Printed: January 14, 2019 File: Grad-Prob-2019.TEX Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221 E-mail address:
More informationAn Introduction to Complex Function Theory
Bruce P. Palka An Introduction to Complex Function Theory With 138 luustrations Springer 1 Contents Preface vü I The Complex Number System 1 1 The Algebra and Geometry of Complex Numbers 1 1.1 The Field
More informationPATTERN CLASSIFICATION
PATTERN CLASSIFICATION Second Edition Richard O. Duda Peter E. Hart David G. Stork A Wiley-lnterscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane Singapore Toronto CONTENTS
More informationGeneral Theory of Large Deviations
Chapter 30 General Theory of Large Deviations A family of random variables follows the large deviations principle if the probability of the variables falling into bad sets, representing large deviations
More informationLarge Deviation Theory. J.M. Swart December 2, 2016
Large Deviation Theory J.M. Swart December 2, 206 2 3 Preface The earliest origins of large deviation theory lie in the work of Boltzmann on entropy in the 870ies and Cramér s theorem from 938 [Cra38].
More informationStochastic-Process Limits
Ward Whitt Stochastic-Process Limits An Introduction to Stochastic-Process Limits and Their Application to Queues With 68 Illustrations Springer Contents Preface vii 1 Experiencing Statistical Regularity
More informationarxiv: v3 [cond-mat.stat-mech] 29 Feb 2012
A basic introduction to large deviations: Theory, applications, simulations arxiv:1106.4146v3 [cond-mat.stat-mech] 29 Feb 2012 Hugo Touchette School of Mathematical Sciences, Queen Mary, University of
More informationErgodicity for Infinite Dimensional Systems
London Mathematical Society Lecture Note Series. 229 Ergodicity for Infinite Dimensional Systems G. DaPrato Scuola Normale Superiore, Pisa J. Zabczyk Polish Academy of Sciences, Warsaw If CAMBRIDGE UNIVERSITY
More informationWiley. Methods and Applications of Linear Models. Regression and the Analysis. of Variance. Third Edition. Ishpeming, Michigan RONALD R.
Methods and Applications of Linear Models Regression and the Analysis of Variance Third Edition RONALD R. HOCKING PenHock Statistical Consultants Ishpeming, Michigan Wiley Contents Preface to the Third
More informationContents LIST OF TABLES... LIST OF FIGURES... xvii. LIST OF LISTINGS... xxi PREFACE. ...xxiii
LIST OF TABLES... xv LIST OF FIGURES... xvii LIST OF LISTINGS... xxi PREFACE...xxiii CHAPTER 1. PERFORMANCE EVALUATION... 1 1.1. Performance evaluation... 1 1.2. Performance versus resources provisioning...
More informationTIME SERIES ANALYSIS. Forecasting and Control. Wiley. Fifth Edition GWILYM M. JENKINS GEORGE E. P. BOX GREGORY C. REINSEL GRETA M.
TIME SERIES ANALYSIS Forecasting and Control Fifth Edition GEORGE E. P. BOX GWILYM M. JENKINS GREGORY C. REINSEL GRETA M. LJUNG Wiley CONTENTS PREFACE TO THE FIFTH EDITION PREFACE TO THE FOURTH EDITION
More informationSpherical Inversion on SL n (R)
Jay Jorgenson Serge Lang Spherical Inversion on SL n (R) Springer Contents Acknowledgments Overview Table of the Decompositions ix xi xvii CHAPTER I Iwasawa Decomposition and Positivity 1 1. The Iwasawa
More informationIntroduction to the Mathematics of Medical Imaging
Introduction to the Mathematics of Medical Imaging Second Edition Charles L. Epstein University of Pennsylvania Philadelphia, Pennsylvania EiaJTL Society for Industrial and Applied Mathematics Philadelphia
More informationA large-deviation principle for Dirichlet posteriors
Bernoulli 6(6), 2000, 02±034 A large-deviation principle for Dirichlet posteriors AYALVADI J. GANESH and NEIL O'CONNELL 2 Microsoft Research, Guildhall Street, Cambridge CB2 3NH, UK. E-mail: ajg@microsoft.com
More informationCourse Description - Master in of Mathematics Comprehensive exam& Thesis Tracks
Course Description - Master in of Mathematics Comprehensive exam& Thesis Tracks 1309701 Theory of ordinary differential equations Review of ODEs, existence and uniqueness of solutions for ODEs, existence
More informationA large deviation principle for a RWRC in a box
A large deviation principle for a RWRC in a box 7th Cornell Probability Summer School Michele Salvi TU Berlin July 12, 2011 Michele Salvi (TU Berlin) An LDP for a RWRC in a nite box July 12, 2011 1 / 15
More informationOptimization: Insights and Applications. Jan Brinkhuis Vladimir Tikhomirov PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD
Optimization: Insights and Applications Jan Brinkhuis Vladimir Tikhomirov PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Contents Preface 0.1 Optimization: insights and applications xiii 0.2 Lunch, dinner,
More informationOn asymptotically efficient simulation of large deviation probabilities
On asymptotically efficient simulation of large deviation probabilities A. B. Dieker and M. Mandjes CWI P.O. Box 94079 1090 GB Amsterdam, the Netherlands and University of Twente Faculty of Mathematical
More informationHI CAMBRIDGE n S P UNIVERSITY PRESS
Infinite-Dimensional Dynamical Systems An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors JAMES C. ROBINSON University of Warwick HI CAMBRIDGE n S P UNIVERSITY PRESS Preface
More informationManfred Einsiedler Thomas Ward. Ergodic Theory. with a view towards Number Theory. ^ Springer
Manfred Einsiedler Thomas Ward Ergodic Theory with a view towards Number Theory ^ Springer 1 Motivation 1 1.1 Examples of Ergodic Behavior 1 1.2 Equidistribution for Polynomials 3 1.3 Szemeredi's Theorem
More informationCondensed Table of Contents for Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control by J. C.
Condensed Table of Contents for Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control by J. C. Spall John Wiley and Sons, Inc., 2003 Preface... xiii 1. Stochastic Search
More informationGeorge G. Roussas University of California, Davis
AN INTRODUCTION TO MEASURE-THEORETIC PROBABILITY George G. Roussas University of California, Davis TABLE OF CONTENTS PREFACE xi CHAPTER I: Certain Classes of Sets, Measurability, and Pointwise Approximation
More informationLarge Deviations for Small-Noise Stochastic Differential Equations
Chapter 22 Large Deviations for Small-Noise Stochastic Differential Equations This lecture is at once the end of our main consideration of diffusions and stochastic calculus, and a first taste of large
More informationUniversity of Southampton Research Repository eprints Soton
University of Southampton Research Repository eprints Soton Copyright and Moral Rights for this thesis are retained by the author and/or other copyright owners. A copy can be downloaded for personal non-commercial
More informationLarge deviations for Poisson random measures and processes with independent increments
tochastic Processes and their Applications 85 (2000) 93 121 www.elsevier.com/locate/spa Large deviations for Poisson random measures and processes with independent increments C. Leonard a;b; a Equipe Modal-X,
More informationLarge Deviations for Small-Noise Stochastic Differential Equations
Chapter 21 Large Deviations for Small-Noise Stochastic Differential Equations This lecture is at once the end of our main consideration of diffusions and stochastic calculus, and a first taste of large
More informationAn almost sure invariance principle for additive functionals of Markov chains
Statistics and Probability Letters 78 2008 854 860 www.elsevier.com/locate/stapro An almost sure invariance principle for additive functionals of Markov chains F. Rassoul-Agha a, T. Seppäläinen b, a Department
More informationStatistical Mechanics
Franz Schwabl Statistical Mechanics Translated by William Brewer Second Edition With 202 Figures, 26 Tables, and 195 Problems 4u Springer Table of Contents 1. Basic Principles 1 1.1 Introduction 1 1.2
More information