Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods (Probability Theory and Stochastic Modelling, 94) - Hardcover

Budhiraja, Amarjit; Dupuis, Paul

Hardcover

ISBN 10: 1493995774 ISBN 13: 9781493995776

Publisher: Springer, 2019

Synopsis

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 this title

About the Author

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.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2019
• Language: English
• ISBN 10: 1493995774
• ISBN 13: 9781493995776
• Binding: Hardcover
• Edition number: 1
• Number of pages: 593