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Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods
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Catalogue Information
Field name
Details
Dewey Class
519.2
Title
Analysis and Approximation of Rare Events ([EBook]) : Representations and Weak Convergence Methods / by Amarjit Budhiraja, Paul Dupuis.
Author
Budhiraja, Amarjit
Added Personal Name
Dupuis, Paul
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : Springer , 2019.
Physical Details
XIX, 574 pages: 14 illus., 1 illus. in color. : online resource.
Series
Probability Theory and Stochastic Modelling
; 94
ISBN
9781493995790
Summary Note
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 note
Preliminaries and elementary examples -- Discrete time processes -- Continuous time processes -- Monte Carlo approximation.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
https://doi.org/10.1007/978-1-4939-9579-0
Links to Related Works
Subject References:
Applied mathematics
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Engineering mathematics
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Mathematical and Computational Engineering
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Numerical Analysis
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Probabilities
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Probability theory and stochastic processes
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Authors:
author
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Budhiraja, Amarjit
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Dupuis, Paul
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Corporate Authors:
SpringerLink (Online service)
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Series:
Probability Theory and Stochastic Modelling
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Classification:
519.2
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519.2 (DDC 23)
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