本书前四章取材于1987年Stroock在麻省理工学院的演讲。它们构成了对大偏差理论基本思想的介绍，并为具有较强分析和概率论背景的高年级研究生提供了一个学期的课程基础。最后两章介绍了各种不一致的结果(第5章)，并概述了允许测试和比较前几章中使用的技术的分析方法(第6章)。本书适合对大偏差感兴趣的研究生和数学研究人员阅读参考。 This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).

前辅文
Preface
Chapter 1 Some Examples
  1.1. The General Idea
  1.2. The Classical Cramér Theorem
  1.3. Schilder's Theorem
  1.4. Two Applications of Schilder's Theorem
Chapter 2 Some Generalities
  2.1. The Large Deviation Principle
  2.2. Large Deviations and Convex Analysis
Chapter 3 General Cramér Theory
  3.1. Preliminary Formulation
  3.2. Sanov's Theorem
  3.3. Cramér's Theorem for Banach Spaces
  3.4. Large Deviations for Gaussian Measures
Chapter 4 Uniform Large Deviations
  4.1. Markov Chains
  4.2. Continuous Time Markov Processes
  4.3. The Wiener Sausage
  4.4. Process Level Large Deviations
Chapter 5 Non-Uniform Results
  5.1. Generalities about the Upper Bound
  5.2. A Little Ergodic Theory
  5.3. The General Symmetric Markov Case
  5.4. Large Deviations for Hypermixing Processes
  5.5. Hypermixing in the Epsilon Markov Case
Chapter 6 Analytic Considerations
  6.1. When Is a Markov Process Hypermixing?
  6.2. Symmetric Diffusions on a Manifold
  6.3. Hypoelliptic Diffusions on a Compact Manifold
Historical Notes and References
Name Index
Bibliography
Frequently Used Notation
Index