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Large Deviations and Applications

S. R. S. Varadhan



CBMS-NSF Regional Conference Series in Applied Mathematics 46

Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.

Contents

Large Deviations; Cramer's Theorem; Multidimensional Version of Cramer's Theorem; An Infinite Dimensional Example: Brownian Motion; The Ventcel-Freidlin Theory; The Exit Problem; Empirical Distributions; The Large Deviation Problem for Empirical Distributions of Markov Processes; Some Properties of Entropy; Upper Bounds; Lower Bounds; Contraction Principle; Application to the Problem of the Wiener Sausage; The Polaron Problem.

1984 / v + 75 pages / Softcover / ISBN-13: 978-0-898711-89-9 / ISBN-10: 0-89871-189-4 /
List Price $42.00 / SIAM/CBMS Member Price $29.40 / Order Code CB46
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