Overview
- 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
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 94)
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Table of contents (17 chapters)
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Front Matter
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Laplace Principle, Relative Entropy, and Elementary Examples
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Front Matter
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Discrete Time Processes
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Front Matter
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Continuous Time Processes
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Front Matter
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Accelerated Monte Carlo for Rare Events
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Front Matter
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Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Analysis and Approximation of Rare Events
Book Subtitle: Representations and Weak Convergence Methods
Authors: Amarjit Budhiraja, Paul Dupuis
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-1-4939-9579-0
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2019
Hardcover ISBN: 978-1-4939-9577-6Published: 11 August 2019
Softcover ISBN: 978-1-4939-9622-3Published: 15 August 2020
eBook ISBN: 978-1-4939-9579-0Published: 10 August 2019
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XIX, 574
Number of Illustrations: 13 b/w illustrations, 1 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Mathematical and Computational Engineering, Numerical Analysis