图书信息
图书目录
Gauss测度（影印版）
暂无简介
作者：
Vladimir I. Bogachev
定价：
169.00 元
出版时间：
2026-03-27
ISBN：
978-7-04-066136-1
物料号：
66136-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
分析
重点项目：
暂无
版面字数：
700.00千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次印刷时间：
2026-01-06
- 前辅文
- Preface
- Chapter 1. Finite Dimensional Gaussian Distributions
- 1.1. Gaussian measures on the real line
- 1.2. Multivariate Gaussian distributions
- 1.3. Hermite polynomials
- 1.4. The Ornstein-Uhlenbeck semigroup
- 1.5. Sobolev classes
- 1.6. Hypercontractivity
- 1.7. Several useful estimates
- 1.8. Convexity inequalities
- 1.9. Characterizations of Gaussian measures
- 1.10. Complements and problems
- Chapter 2.Infinite Dimensional Gaussian Distributions
- 2.1. Cylindrical sets
- 2.2. Basic definitions
- 2.3. Examples
- 2.4. The Cameron-Martin space
- 2.5. Zero-one laws
- 2.6. Separability and oscillations
- 2.7. Equivalence and singularity
- 2.8. Measurable seminorms
- 2.9. The Ornstein-Uhlenbeck semigroup
- 2.10.Measurable linear functionals
- 2.11. Stochastic integrals
- 2.12. Complements and problems
- Chapter 3. Radon Gaussian Measures
- 3.1. Radon measures
- 3.2. Basic properties of Radon Gaussian measures
- 3.3. Gaussian covariances
- 3.4. The structure of Radon Gaussian measures
- 3.5. Gaussian series
- 3.6. Supports of Gaussian measures
- 3.7. Measurable linear operators
- 3.8. Weak convergence of Gaussian measures
- 3.9. Abstract Wiener spaces
- 3.10. Conditional measures and conditional expectations
- 3.11. Complements and problems
- Chapter 4. Convexity of Gaussian Measures
- 4.1. Gaussian symmetrization
- 4.2. Ehrhard's inequality
- 4.3. Isoperimetric inequalities
- 4.4. Convex functions
- 4.5. H-Lipschitzian functions
- 4.6. Correlation inequalities
- 4.7. The Onsager-Machlup functions
- 4.8. Small ball probabilities
- 4.9. Large deviations
- 4.10. Complements and problems
- Chapter 5. Sobolev Classes over Gaussian Measures
- 5.1. Integration by parts
- 5.2. The Sobolev classes Wp,r and Dp,n
- 5.3. The Sobolev classes HP,r
- 5.4. Properties of Sobolev classes and examples
- 5.5. The logarithmic Sobolev inequality
- 5.6. Multipliers and Meyer's inequalities
- 5.7. Equivalence of different definitions
- 5.8. Divergence of vector fields
- 5.9. Gaussian capacities
- 5.10 Measurable polynomials
- 5.11. Differentiability of H-Lipschitzian functions
- 5.12. Complements and problems
- Chapter 6. Nonlinear Transformations of Gaussian Measures
- 6.1. Auxiliary results
- 6.2. Measurable linear automorphisms
- 6.3. Linear transformations
- 6.4. Radon-Nikodym densities
- 6.5. Examples of equivalent measures and linear transformations
- 6.6. Nonlinear transformations
- 6.7. Examples of nonlinear transformations
- 6.8. Finite dimensional mappings
- 6.9. Malliavin's method
- 6.10. Surface measures
- 6.11. Complements and problems
- Chapter 7. Applications
- 7.1. Trajectories of Gaussian processes
- 7.2. Infinite dimensional Wiener processes
- 7.3. Logarithmic gradients
- 7.4. Spherically symmetric measures
- 7.5. Infinite dimensional diffusions
- 7.6. Complements and problems
- Appendix A. Locally Convex Spaces, Operators, and Measures
- A.1. Locally convex spaces
- A.2. Linear operators
- A.3. Measures and measurability
- Bibliographical Comments
- References
- Index
