A Weak Convergence Approach To The Theory Of Large Deviations
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A Weak Convergence Approach To The Theory Of Large Deviations
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Author : Paul Dupuis
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09
A Weak Convergence Approach To The Theory Of Large Deviations written by Paul Dupuis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Mathematics categories.
Applies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.
A Weak Convergence Approach To The Theory Of Large Deviations
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Author : Paul Dupuis
language : en
Publisher: John Wiley & Sons
Release Date : 1997-02-27
A Weak Convergence Approach To The Theory Of Large Deviations written by Paul Dupuis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-27 with Mathematics categories.
Applies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.
Large Deviations And Idempotent Probability
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Author : Anatolii Puhalskii
language : en
Publisher: CRC Press
Release Date : 2001-05-07
Large Deviations And Idempotent Probability written by Anatolii Puhalskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-07 with Business & Economics categories.
In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak
Analysis And Approximation Of Rare Events
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Author : Amarjit Budhiraja
language : en
Publisher: Springer
Release Date : 2019-08-10
Analysis And Approximation Of Rare Events written by Amarjit Budhiraja and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-10 with Mathematics categories.
This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Large Deviations For Stochastic Processes
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Author : Jin Feng
language : en
Publisher:
Release Date : 2014-05-21
Large Deviations For Stochastic Processes written by Jin Feng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-21 with MATHEMATICS categories.
This work is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts.
Large Deviations
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Author : Frank den Hollander
language : en
Publisher: American Mathematical Soc.
Release Date :
Large Deviations written by Frank den Hollander and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Stochastic Differential Equations
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Author : Peter H. Baxendale
language : en
Publisher: World Scientific
Release Date : 2007
Stochastic Differential Equations written by Peter H. Baxendale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations. The other papers in this volume were specially written for the occasion of Prof RozovskiiOCOs 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives."
Uncertainty In Economic Theory
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Author : Itzhak Gilboa
language : en
Publisher: Routledge
Release Date : 2004-08-02
Uncertainty In Economic Theory written by Itzhak Gilboa and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-02 with Business & Economics categories.
This volume brings together important papers, coupled with new introductions, in the massively influential area of uncertainty in economic theory. Seminal papers are available together for the first time in book format, with new introductions and under the steely editorship of Itzhak Gilboa - this book is a useful reference tool for economists all over the globe.
Large Deviations And Applications
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Author : S. R. S. Varadhan
language : en
Publisher: SIAM
Release Date : 1984-01-01
Large Deviations And Applications written by S. R. S. Varadhan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
Stochastic Analysis And Diffusion Processes
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Author : Gopinath Kallianpur
language : en
Publisher: OUP Oxford
Release Date : 2014-01-09
Stochastic Analysis And Diffusion Processes written by Gopinath Kallianpur and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.