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

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Overview

This book presents a new and widely applicable method to the theory of large deviations. This approach allows large deviation problems, which are nonlinear, to be reduced to problems that are essentially linear in nature (weak convergence improbability). The authors develop the weak convergence method from scratch, illustrate via several basic examples and then apply it to a number of sophisticated models. Much of the material in the text is being published for the first time.
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Editorial Reviews

Booknews
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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Product Details

Meet 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.

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Table of Contents

1 Formulation of Large Deviation Theory in Terms of the Laplace Principle 1
2 First Example: Sanov's Theorem 48
3 Second Example: Mogulskii's Theorem 65
4 Representation Formulas for Other Stochastic Processes 92
5 Compactness and Limit Properties for the Random Walk Model 127
6 Laplace Principle for the Random Walk Model with Continuous Statistics 149
7 Laplace Principle for the Random Walk Model with Discontinuous Statistics 216
8 Laplace Principle for the Empirical Measures of a Markov Chain 275
9 Extensions of the Laplace Principle for the Empirical Measures of a Markov Chain 320
10 Laplace Principle for Continuous-Time Markov Processes with Continuous Statistics 350
App. A Background Material 371
App. B Deriving the Representation Formulas via Measure Theory 400
App. C Proofs of a Number of Results 405
App. D Convex Functions 431
App. E Proof of Theorem 5.3.5 When Condition 5.4.1 Replaces Condition 5.3.1 449
Bibliography 458
Notation Index 463
Author Index 467
Subject Index 469
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