عنوان

Analysis and approximation of rare events

9781493995790

E340

انگلیسی

Analysis and approximation of rare events

representations and weak convergence methods

Amarjit Budhiraja, Paul Dupuis

New York, NY

Springer

2019

xix, 574 p.

(Probability Theory and Stochastic Modelling

v. 94)

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

Includes bibliographical references and index

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

Approximation theory

Convergence

a03

a05

Budhiraja, Amarjit

Dupuis, Paul

Iran

University of Tehran. Library of College of Science

20211221

UT_SCI_BL_DB_1002486_0001.pdf

e

BL

278840

a

Y