Large Deviations and Applications

✍ Scribed by S. R. S. Varadhan

• Publisher: Society for Industrial Mathematics
• Year: 1987
• Tongue: English
• Leaves: 84
• Series: CBMS-NSF Regional Conference Series in Applied Mathematics
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Large Deviations and Applications......Page 3
Contents......Page 5
Preface......Page 7
Section 1 Introduction......Page 9
Section 2 Large Deviations......Page 11
Section 3 Cramer's Theorem......Page 15
Section 4 Multidimensional Version of Cramer's Theorem......Page 19
Section 5 An Infinite Dimensional Example: Brownian Motion......Page 23
Section 6 The Ventcel-Freidlin Theory......Page 27
Section 7 The Exit Problem......Page 33
Section 8 Empirical Distributions......Page 39
Section 9 The Large Deviation Problem For Empirical Distributions of Markov Processes......Page 41
Section 10 Some Properties of Entropy......Page 43
Section 11 Upper Bounds......Page 49
Section 12 Lower Bounds......Page 57
Section 13 Contraction Principle......Page 63
Section 14 Application to the Problem of the Wiener Sausage......Page 69
Section 15 The Polaron Problem......Page 77
Section 16 Bibliographical Remarks......Page 81
References......Page 83