Analysis and Approximation of Rare Events
Representations and Weak Convergence Methods
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Beschreibung
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 thedesign 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.
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.
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
Autor*in
Amarjit Budhiraja
Themen in »Analysis and Approximation of Rare Events«
Discrete time processes Monte Carlo Approximation large deviation principle weak convergence methods Rare events large deviation moderate deviation weak convergence relative entropy stochastic analysis representation formulas
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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)
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