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.
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 Continuous Statistics.
Laplace Principle for the Random Walk Model with Discontinuous Statistics.
Laplace Principle for the Empirical Measures of a Markov Chain.
Extensions of the Laplace Principle for the Empirical Measures of a Markov Chain.
Laplace Principle for Continuous–Time Markov Processes with Continuous Statistics.
RICHARD S. ELLIS is a professor in the Department of Mathematics and Statistics at the University of Massachusetts at Amherst.