基本信息 书名:马尔科夫过程-布朗运动和时间对称 定价：69元 作者:钟开来 (Kai Lai Chung), John B.Walsh 出版社：世界图书出版公司北京公司 出版日期：2013-10-01 ISBN：9787510061462 字数： 页码：431 版次：2 装帧：平装 开本：24开 商品重量： 编辑推荐 《马尔科夫过程、布朗运动和时间对称(第2版)(英文版)》由世界图书出版公司北京公司出版。 内容提要 《马尔科夫过程、布朗运动和时间对称(第2版)(英文版)》是基于过去20年间的几份讲义一些部分创作而成，其原型是作者于1970年春天的一学期讲义。书中旨在将马尔科夫过程的一些的特性，特别地，用最少的预备知识和技巧讲述了布朗运动。这新的版本新增加了9章，包括新的练习、参考资料和原来版本的多处修订。 目录 Preface to the New Edition Preface to the First Edition Chapter 1 Markov Process 1.1. Markov Property 1.2. Transition Function 1.3. Optional Times 1.4. Martingale Theorems 1.5. Progressive Measurability and the Section Theorem Exercises Notes on Chapter 1 Chapter2 Basic Properties 2.1. Martingale Connection 2.2. Feller Process Exercises 2.3. Strong Markov Property and Right Continuity of Fields Exercises 2.4. Moderate Markov Property and Quasi Left Continuity Exercises Notes on Chapter 2 Chapter 3 Hunt Process 3.1. Defining Properties Exercises 3.2. Analysis of Excessive Functions Exercises 3.3. Hitting Times 3.4. Balayage and Fundamental Structure Exercises 3.5. Fine Properties Exercises 3.6. Decreasing Limits Exercises 3.7. Recurrence and Transience Exercises 3.8. Hypothesis (B) Exercises Notes on Chapter 3 Chapter4 Brownian Motion 4.1. Spatial Homogeneity Exercises 4.2. Preliminary Properties of Brownian Motion Exercises 4.3. Harmonic Function Exercises 4.4. Dirichlet Problem Exercises 4.5. Superharmonic Function and Supermartingale Exercises 4.6. The Role of the Laplacian Exercises 4.7. The Feynrnan-Kac Functional and the Schrodinger Equation Exercises Notes on Chapter 4 Chapter 5 Potential Developments 5.1. Quitting Time and Equilibrium Measure Exercises 5.2. Some Principles of Potential Theory Exercises Notes on Chapter 5 Chapter 6 Generalities 6.1 Essential Limits 6.2 Penetration Times 6.3 General Theory Exercises Notes on Chapter 6 Chapter 7 Markov Chains: a Fireside Chat 7.1 Basic Examples Notes on Chapter 7 Chapter 8 Ray Processes 8.1 Ray Resolvents and Semigroups 8.2 Branching Points 8.3 The Ray Processes 8.4 Jumps and Branching Points 8.5 Martingales on the Ray Space 8.6 A Feller Property of px 8.7 Jumps Without Branching Points 8.8 Bounded Entrance Laws 8.9 Regular Supermedian Functions 8.10 Ray-Knight Compactifications: Why Every Markov Process is a Ray Process at Heart 8.11 Useless Sets 8.12 Hunt Processes and Standard Processes 8.13 Separation and Supermedian Functions 8.14 Examples Exercises Notes on Chapter 8 Chapter9 Application to Markov Chains 9.1 Compactifications of Markov Chains 9.2 Elementary Path Properties of Markov Chains 9.3 Stable and Instantaneous States 9.4 A Second Look at the Examples of Chapter 7 Exercises Notes on Chapter 9 Chapter 10 Time Reversal 10.1 The Loose Transition Function 10.2 Improving the Resolvent 10.3 Proof of Theorem 10.1 10.4 Removing Hypotheses (H1) and (H2) Notes on Chapter 10 Chapter 11 h-Transforms 11.1 Branching Points 11.2 h-Transforms 11.3 Construction of the h-processes 11.4 Minimal Excessive Functions and the Invariant Field 11.5 Last Et and Co-optional Times 11.6 Reversing h-Transforms Exercises Notes on Chapter 11 Chapter 12 Death and Transfiguration: A Fireside Chat Exercises Notes on Chapter 12 Chapter 13 Processes in Duality 13.1 Formal Duality 13.2 Dual Processes 13.3 Excessive Measures 13.4 Simple Time Reversal 13.5 The Moderate Markov Property 13.6 Dual Quantities 13.7 Small Sets and Regular Points 13.8 Duality and h-Transforms Exercises 13.9 Reversal From a Random Time 13. 10 Xζ-: Limits at the Lifetime 13.11 Balayage and Potentials of Measures 13. t2 The Interior Reduite of a Function 13.13 Quasi-left-continuity, Hypothesis (B), and Reduites 13.14 Fine Symmetry 13.15 Capacities and Last Et Times Exercises Notes on Chapter 13 Chapter 14 The Martin Boundary 14.1 Hypotheses 14.2 The Martin Kernel and the Martin Space 14.3 Minimal Points and Boundary Limits 14.4 The Martin Representation 14.5 Applications 14.6 The Martin Boundary for Brownian Motion 14.7 The Dirichlet Problem in the Martin Space Exercises Notes on Chapter 14 Chapter 15 The Basis of Duality: A Fireside Chat 15.1 Duality Measures 15.2 The Cofine Topology Notes on Chapter 15 Bibliography Index 作者介绍 作者：（美国）钟开来（Kai Lai Chung） （美国）John B.Walsh 序言
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