《連續鞅和布朗運動（第3版）》是2018年世界圖書出版公司出版的著作，作者是[法] Daniel，Revuz（D.勒維）。
基本介紹
- 中文名：《連續鞅和布朗運動（第3版）》
- 作者：[法]Daniel，Revuz（D.勒維）
- ISBN：9787519247706
- 出版社：世界圖書出版公司
- 出版時間：2018-08-01
內容簡介,目錄,
內容簡介
本書是一部講述隨機過程及布朗運動的經典教材，書中詳盡介紹了布朗運動的概念、技巧和方法，大量的習題使得書中的內容更加充實。證明詳細並講究技巧，研究生階段的學生能夠理解本書的大多數內容。書中的計算內容可以作為基礎計算的訓練材料，為進入科研階段的研究生提供了充分的預備知識。讀者對象：適用於機率論及隨機過程方向的研究生，也是相關專業科研人員的案頭參考書。
目錄
Chapter 0. Preliminaries
1.Basic Notation
2.Monotone Class Theorem
3.Completion
4.Functions of Finite Variation and Stieltjes Integrals
5.Weak Convergence in Metric Spaces
6.Gaussian and Other Random Variables
Chapter Ⅰ.Introduction
1.Examples of Stochastic Processes. Brownian Motion
2.Local Properties of Brownian Paths
3.Canonical Processes and Gaussian Processes
4.Filtrations and Stopping Times
Notes and Comments
Chapter Ⅱ.Martingales
1.Definitions, Maximal Inequalities and Applications
2.Convergence and Regularization Theorems
3.Optional Stopping Theorem
Notes and Comments
Chapter Ⅲ.Markov Processes
1.Basic Definitions
2.Feller Processes
3.Strong Markov Property
4.Summary of Results on Levy Processes
Notes and Comments
Chapter Ⅳ.Stochastic Integration
1.Quadratic Variations
2.Stochastic Integrals
3.Ito's Formula and First Applications
4.Burkholder-Davis-Gundy Inequalities
5.Predictable Processes
Notes and Comments
Chapter Ⅴ.Representation of Martingales
1.Continuous Martingales as Time-changed Brownian Motions
2.Conformal Martingales and Planar Brownian Motion
3.Brownian Martingales
4.Integral Representations
Notes and Comments
Chapter Ⅵ.Local Times
1.Definition and First Properties
2.The Local Time of Brownian Motion
3.The Three-Dimensional Bessel Process
4.First Order Calculus
5.The Skorokhod Stopping Problem
Notes and Comments
Chapter Ⅶ.Generators and Time Reversal
1.Infinitesimal Generators
2.Diffusions and It6 Processes
3.Linear Continuous Markov Processes
4.Time Reversal and Applications
Notes and Comments
Chapter Ⅷ.Girsanov's Theorem and First Applications
1.Girsanov's Theorem
2.Application of Girsanov's Theorem to the Study of Wiener's Space
3.Functionals and Transformations of Diffusion Processes
Notes and Comments
Chapter Ⅸ.Stochastic Differential Equations
1.Formal Definitions and Uniqueness
2.Existence and Uniqueness in the Case of Lipschitz Coefficients
3.The Case of Holder Coefficients in Dimension One
Notes and Comments
Chapter Ⅹ.Additive Functionals of Brownian Motion
1.General Definitions
2.Representation Theorem for Additive Functionals of Linear Brownian Motion
3.Ergodic Theorems for Additive Functionals
4.Asymptotic Results for the Planar Brownian Motion
Notes and Comments
Chapter Ⅺ.Bessel Processes and Ray-Knight Theorems
1.Bessel Processes
2.Ray-Knight Theorems
3.Bessel Bridges
Notes and Comments
Chapter Ⅻ. Excursions
1.Prerequisites on Poisson Point Processes
2.The Excursion Process of Brownian Motion
3.Excursions Straddling a Given Time
4.Descriptions of It6's Measure and Applications
Notes and Comments
Chapter ⅩⅢ.Limit Theorems in Distribution
1.Convergence in Distribution
2.Asymptotic Behavior of Additive Functionals of Brownian Motion
3.Asymptotic Properties of Planar Brownian Motion
Notes and Comments
Appendix
1.Gronwall's Lemma
2.Distributions
3.Convex Functions
4.Hausdorff Measures and Dimension
5.Ergodic Theory
6.Probabilities on Function Spaces
7.Bessel Functions
8.Sturm-Liouville Equation
Bibliography
Index of Notation
Index of Terms
Catalogue
