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A Weak Convergence Approach to the Theory of Large Deviations

Author: Paul Dupuis

Publisher: John Wiley & Sons

Published: 2011-09-09

Total Pages: 506

ISBN-13: 1118165896

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

Author: Anatolii Puhalskii

Publisher: CRC Press

Published: 2001-05-07

Total Pages: 515

ISBN-13: 1420035800

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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

A Weak Convergence Approach to the Theory of Large Deviations

Author: Paul Dupuis

Publisher: Wiley-Interscience

Published: 1997-02-27

Total Pages: 504

ISBN-13: 9780471076728

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A Weak Convergence Approach to the Theory of Large Deviations

Author: Paul Dupuis

Publisher: John Wiley & Sons

Published: 1997-02-27

Total Pages: 522

ISBN-13: 9780471076728

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Large Deviations for Stochastic Processes

Author: Jin Feng

Publisher: American Mathematical Soc.

Published: 2015-02-03

Total Pages: 426

ISBN-13: 1470418703

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The book 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. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.

Analysis and Approximation of Rare Events

Author: Amarjit Budhiraja

Publisher: Springer

Published: 2019-08-10

Total Pages: 574

ISBN-13: 1493995790

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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 Techniques and Applications

Author: Amir Dembo

Publisher: Springer Science & Business Media

Published: 2009-11-03

Total Pages: 409

ISBN-13: 3642033113

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Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition.

Large Deviations

Author: Frank Hollander

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 164

ISBN-13: 9780821844359

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Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.

Large Deviations

Author:

Publisher: Academic Press

Published: 1989-06-21

Total Pages: 306

ISBN-13: 9780080874579

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The first four chapters of this volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).

Large Deviations

Author: Jean-Dominique Deuschel

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 298

ISBN-13: 082182757X

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This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).