Analysis and Approximation of Rare Events : Representations and Weak Convergence Methods

Amarjit Budhiraja

ISBN 10: 1493995774 / ISBN 13: 9781493995776

Editore: Springer, Springer, 2019

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9781493995776

Dati bibliografici

• Titolo: Analysis and Approximation of Rare Events : Representations and Weak Convergence Methods
• Editore: Springer, Springer
• Data di pubblicazione: 2019
• Lingua: Inglese
• ISBN 10: 1493995774
• ISBN 13: 9781493995776
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 38 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 38 millimetri di profondità
• Peso: 1051 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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.