Analysis and Approximation of Rare Events
Representations and Weak Convergence Methods
Authors: Budhiraja, Amarjit, Dupuis, Paul
Free Preview- Illustrates the use of these methods using a wide variety of discrete and continuous time models
- Timely and important topic with significant developments over the last 15 years
- Includes both theory and links with applications
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- About this book
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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.
- About the authors
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Amarjit Budhiraja is a Professor of Statistics and Operations Research at the University of North Carolina at Chapel Hill. He is a Fellow of the IMS. His research interests include stochastic analysis, the theory of large deviations, stochastic networks and stochastic nonlinear filtering.
Paul Dupuis is the IBM Professor of Applied Mathematics at Brown University and a Fellow of the AMS, SIAM and IMS. His research interests include stochastic control, the theory of large deviations and numerical methods. - Reviews
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“The book is very well organized and the structure of each chapter is helpful: notation, assumptions, statements, examples, proofs and comments are clearly separated. … this makes the book a good reference for researchers interested in rare event analysis and approximation.” (Charles-Edouard Bréhier, Mathematical Reviews, August, 2020)
“The current book requires a solid background in weak convergence of probability measures and stochastic analysis, and it is intended for advanced graduate students, post-doctoral fellows and researchers working in this area.” (Anatoliy Swishchuk, zbMATH 1427.60003, 2020)
- Table of contents (17 chapters)
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General Theory
Pages 3-29
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Relative Entropy and Tightness of Measures
Pages 31-47
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Examples of Representations and Their Application
Pages 49-76
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Recursive Markov Systems with Small Noise
Pages 79-117
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Moderate Deviations for Recursive Markov Systems
Pages 119-149
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Table of contents (17 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Analysis and Approximation of Rare Events
- Book Subtitle
- Representations and Weak Convergence Methods
- Authors
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- Amarjit Budhiraja
- Paul Dupuis
- Series Title
- Probability Theory and Stochastic Modelling
- Series Volume
- 94
- Copyright
- 2019
- Publisher
- Springer US
- Copyright Holder
- Springer Science+Business Media, LLC, part of Springer Nature
- eBook ISBN
- 978-1-4939-9579-0
- DOI
- 10.1007/978-1-4939-9579-0
- Hardcover ISBN
- 978-1-4939-9577-6
- Softcover ISBN
- 978-1-4939-9622-3
- Series ISSN
- 2199-3130
- Edition Number
- 1
- Number of Pages
- XIX, 574
- Number of Illustrations
- 13 b/w illustrations, 1 illustrations in colour
- Topics
