Large deviations and applications : Consists of notes based on lectures given at a conference at the University of Southern Illinois at Carbondale during June 1982

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. 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