- 连续鞅和布朗运动(第3版)(英文版)
- - 作者：(法)D.勒维//M.约尔
  - 出版社：世界图书出版公司
  - ISBN：9787519247706
  - 出版日期：2018/08/01
  - 页数：606
- 售价：47.6

内容大纲
D.勒维、M.约尔著的《连续鞅和布朗运动(第3版)(英文版)》是一部讲述随机过程及布朗运动的经典教材，书中详尽介绍了布朗运动的概念、技巧和方法，大量的习题使得书中的内容更加充实。证明详细并讲究技巧，研究生阶段的学生能够理解本书的大多数内容。书中的计算内容可以作为基础计算的训练材料，为进入科研阶段的研究生提供了充分的预备知识。本书适用于概率论及随机过程方向的研究生，也是相关专业科研人员的案头参考书。
作者介绍
目录
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

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目