鐘開來著的《馬爾科夫過程布朗運動和時間對稱(第2版)》是基於過去20年間的幾份講義一些部分創作而成，其原型是作者於1970年春天的一學期講義。書中旨在將馬爾科夫過程的一些*好的特性，特別地，用*少的預備知識和技巧講述了布朗運動。這新的版本新增加了9章，包括新的練習、參考資料和原來版本的多處修訂。目次：馬爾科夫過程；基本上性質；Hunt過程；布朗運動；勢發展；綜述；馬爾科夫鏈；放射過程；馬爾科夫鏈的應用；時間逆轉；h－變換；滅亡與變形；對偶過程；Martin邊界。讀者對像：數學、物理專業的研究生、老師和相關的科研人員。

Preface to the New Edition
Prefaee to the First Edition
Chapter 1
Markov Process
1.1. Markov Property
1.2. Transition Funotion
1.3. Optional.Times
1.4. Martingale Theorems
1.5. Progressive Measurability and the Section Theorem
Exercises
Notes On Chapter 1
Chapter 2
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
Exerclses
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. Harmonie Function
Exercises
4.4. Dirichlet Problem
Exetcises
4.5. Superharmomc Function and Supermartingale
Exercises
4.6. The Role ofthe Laplacian
Exercises
4.7. The Feynman-Kac Functional and the Schrodinger Equation
Exercises
Notes on Chapter 4
Chapter 5
Potential Developments
5.1. QuittingTime and Equilibrium Measure
Exercises
5.2. Some Principles of Potential Theory
Exercises
Notes on Chapter 5
Chapter 6
Generalities
6.1. Essenfial Limits
6.2. Penetration Tiriles
6.3. General Theory
Exemises
Notes on Chapter 6
Chapter7
Markov Chains：a Fireside Chat
7.1 Basic Examples
Nores on Chapter 7
Chapter8
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 FetierProperty of Px
8.7. Jumps Without Branching Points
8.8. Bounded En~ance Laws
8.9. Regutar Snpetmedian Functions
8.10. Ray-Knight Compactifications：Why Every Markov Process is a Ray
Process at Hcart
8.11. Useless Sets
8.12. Hunt Processes and Standard Processes
8.13. Separation and Supermedian Funcfions
8 14. Examples
Exercises
Nores on Chapter 8
Chapter9
Application to Markov Chains
9.1. Compactifications of Markov Chaias
9.2. Elementary Path Properties of Markov chaias
9 3. Stable and Instantaneous States
9.4. A Second Look at the Examples ofChapter7
Exercises
Notes on Chapter8
Chapter 10
Time Reversal
10.1. the Loose nansition Function
10.2. Improving the Resolvent
10.3. PtoofofTheorem 10.1
10.4. Removing Hypotheses（H1）and（H2）
Nores on Chapter 10
Chapter 11
h-Transforms
11.1. Branching Points
11.2. h-Transforms
11.3. Construction ofthe h-Processes
11.4. Minimal Excessive Functions and the Invariant Field
11.5. Last Exit and Co-optional Times
11.6. Reversing h-Transforms
Exercises
Nores 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 Mensures
13.4. Simple Time Reversal
13.5. The Moderate Markov Property
13.6. Dual Quantities
13.7. SmalJ Sets and Regular Points
13.8. Duality and h-Transforms
Exercises
13.9. Reversal Ftom a Random Time
13.10. X_：Limits at the Lifetime
13.11. Balayage and Potentials of Measures
13.12. The Interior Reduite of a Function
13.13. Quasi-left-confinuity，Hypothesis（B），and Reduites
13.14. Fine Symmetry
13.15. Capacities and Last Exit Times
Exercises
Nores on Chapter 13
Chapter 14
The Martin Boundary
14.1. Hypotheses
14.2. The Martin Kerneland 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 Morion
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