A Weak Convergence Approach to the Theory of Large Deviations

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. 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. 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. Applies the well-developed tools of the theory of weak convergence of probability measures to large deviation analysis—a consistent new approach

The theory of large deviations, one of the most dynamic topics in probability today, studies rare events in stochastic systems. The nonlinear nature of the theory contributes both to its richness and difficulty. This innovative text demonstrates how to employ the well-established linear techniques of weak convergence theory to prove large deviation results. Beginning with a step-by-step development of the approach, the book skillfully guides readers through models of increasing complexity covering a wide variety of random variable-level and process-level problems. Representation formulas for large deviation-type expectations are a key tool and are developed systematically for discrete-time problems.

Accessible to anyone who has a knowledge of measure theory and measure-theoretic probability, A Weak Convergence Approach to the Theory of Large Deviations is important reading for both students and researchers.