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Analysis and approximation of rare e...

Budhiraja, Amarjit.

Analysis and approximation of rare eventsrepresentations and weak convergence methods /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analysis and approximation of rare eventsby Amarjit Budhiraja, Paul Dupuis.
Reminder of title:	representations and weak convergence methods /
Author:	Budhiraja, Amarjit.
other author:	Dupuis, Paul.
Published:	New York, NY :Springer US :2019.
Description:	xix, 574 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Approximation theory.
Online resource:	https://doi.org/10.1007/978-1-4939-9579-0
ISBN:	9781493995790$q(electronic bk.)

Analysis and approximation of rare eventsrepresentations and weak convergence methods /
Budhiraja, Amarjit.

Analysis and approximation of rare eventsrepresentations and weak convergence methods /[electronic resource] :by Amarjit Budhiraja, Paul Dupuis. - New York, NY :Springer US :2019. - xix, 574 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.942199-3130 ;. - Probability theory and stochastic modelling ;v.70..

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

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.

ISBN: 9781493995790$q(electronic bk.)

Standard No.: 10.1007/978-1-4939-9579-0doiSubjects--Topical Terms:

185327
Approximation theory.

LC Class. No.: QA221 / .B83 2019

Dewey Class. No.: 511.4

Analysis and approximation of rare eventsrepresentations and weak convergence methods /
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490 1 $a Probability theory and stochastic modelling, $x 2199-3130 ; $v v.94
505 0 $a Preliminaries and elementary examples -- Discrete time processes -- Continuous time processes -- Monte Carlo approximation.
520 $a 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.
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