Analysis and Approximation of Rare Events

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Sprache: Englisch

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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 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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

Preliminaries and elementary examples.- Discrete time processes.- Continuous time processes.- Monte Carlo approximation.¿

Details

Erscheinungsjahr:	2019
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Probability Theory and Stochastic Modelling
Inhalt:	xix 574 S. 13 s/w Illustr. 1 farbige Illustr. 574 p. 14 illus. 1 illus. in color.
ISBN-13:	9781493995776
ISBN-10:	1493995774
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Dupuis, Paul Budhiraja, Amarjit
Auflage:	1st ed. 2019
Hersteller:	Springer US Springer US, New York, N.Y. Probability Theory and Stochastic Modelling
Maße:	241 x 160 x 38 mm
Von/Mit:	Paul Dupuis (u. a.)
Erscheinungsdatum:	11.08.2019
Gewicht:	1,051 kg

Artikel-ID: 115848953