A Weak Convergence Approach to the Theory of Large Deviations / Edition 1

by Paul Dupuis, Richard S. Ellis

Overview

Applies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis—a consistentnew approach

The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems.

Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.

Product Details

ISBN-13:	9780471076728
Publisher:	Wiley
Publication date:	02/27/1997
Series:	Wiley Series in Probability and Statistics , #313
Pages:	504
Product dimensions:	6.50(w) x 9.45(h) x 1.10(d)

About the Author

PAUL DUPUIS is a professor in the Division of Applied Mathematics at Brown University in Providence, Rhode Island.

RICHARD S. ELLIS is a professor in the Department of Mathematics and Statistics at the University of Massachusetts at Amherst.

Table of Contents

Formulation of Large Deviation Theory in Terms of the LaplacePrinciple.

First Example: Sanov's Theorem.

Second Example: Mogulskii's Theorem.

Representation Formulas for Other Stochastic Processes.

Compactness and Limit Properties for the Random Walk Model.

Laplace Principle for the Random Walk Model with ContinuousStatistics.

Laplace Principle for the Random Walk Model with DiscontinuousStatistics.

Laplace Principle for the Empirical Measures of a MarkovChain.

Extensions of the Laplace Principle for the Empirical Measures of aMarkov Chain.

Laplace Principle for Continuous-Time Markov Processes withContinuous Statistics.

Appendices.

Bibliography.

Indexes.

Editorial Reviews

Applies the well established linear techniques of weak convergence theory to the nonlinear theory of large derivations, thus overcoming some of its difficulties while continuing to exploit its richness in investigating rare events in stochastic systems. Develops the approach step by step through increasing complexity covering a wide range of problems at the both the variable and the process levels. Assumes a knowledge of measure theory and measure-theoretic probability. Annotation c. by Book News, Inc., Portland, Or.

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