大偏差（影印版）
定价：￥135.00
作者： Jean-Dominique Deuschel，Daniel W.Stroock
出版社：高等教育出版社
- 高等教育出版社
- 9787040630992
- 1版
- 47266365-7
- 特殊
- 470
- 理学
- 数学类
- 数学类
- 本科 研究生及以上
目录
目录
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
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
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
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
