Analysis and Approximation of Rare Events : Representations and Weak Convergence Methods / by Amarjit Budhiraja, Paul Dupuis.

Format:

Book

Author/Creator:

Budhiraja, Amarjit, author.

Dupuis, Paul, author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (Springer-11649)

Probability theory and stochastic modelling 2199-3130 ; 94.

Probability Theory and Stochastic Modelling, 2199-3130 ; 94

Language:

English

Subjects (All):

Probabilities.

Applied mathematics.

Engineering mathematics.

Numerical analysis.

Probability Theory and Stochastic Processes.

Mathematical and Computational Engineering.

Numerical Analysis.

Local Subjects:

Probability Theory and Stochastic Processes.

Mathematical and Computational Engineering.

Numerical Analysis.

Physical Description:

1 online resource (XIX, 574 pages) : 14 illustrations, 1 illustrations in color.

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

New York, NY : Springer US : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

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.

Contents:

Preliminaries and elementary examples

Discrete time processes

Continuous time processes

Monte Carlo approximation.

Other Format:

Printed edition:

ISBN:

978-1-4939-9579-0

9781493995790

OCLC:

1112419403

Access Restriction:

Restricted for use by site license.