正版新书]经典数学教材(影印版):马尔科夫过程、布朗运动和时

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

This book consists of two parts， to be called Part I and Part n. Part I， Chapters l through 5， is essentially a new edition of Kai Lai Chung's Lec-tures from Markov Processes to Brownian Motion （1982）. He has corrected a number of misprints in the original edition， and has inserted a few references and remarks， of which he says， "The latter must be regarded as randomly selected since twenty-some years is a long time to retrace steps . . ." This part introduces strong Markov processes and their potential theory. In particular，it studies Brownian motion， and shows how it generates classical potential theory.　　Part II， Chapters 6 through 15， began life as a set of notes for a series of lectures on time reversal and duality given at the University of Paris. I originally planned to add the essential parts of these notes to this edition to show how the reversal of time-the retracing of steps-explained so much about Markov processes and their potential theory. But like many others， I learned that the inessential parts of a cherished manuscript form at most a fuzzy empty set， while the essential parts include everything that should have been in the original， even if it wasn't. In short， this， like Topsy， just grow'd.　　Indeed， reversal and duality are best understood in light of Ray processes and the Ray-Knight compactification. But it is fitting that a study of symmetry be symmetrical itself， so once I had included the Ray compactification， I had to include its mirror image， the Martin boundary. This was followed by a host of examples， remarks and theorems to show how these new ideas influence the theory and practice developed in the first part. The result was the present Part II.　　In a sense， Part II deals with the same subjects as Pan I， but more narrowly: using Part I for a general understanding， we are free to focus on the effects of time reversal， duality， and time-symmetry on potential theory. Certain theo-rems in Part I are re-proved in Part II under slightly weaker hypotheses. This . is not because I want to generalize the theorems， but because I want to show　　them in a different light: the proofs in Part II are quite different from those of Part I.　　……

钟开来著的《马尔科夫过程布朗运动和时间对称(第2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最好的特性，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。目次：马尔科夫过程；基本上性质；Hunt过程；布朗运动；势发展；综述；马尔科夫链；放射过程；马尔科夫链的应用；时间逆转；h－变换；灭亡与变形；对偶过程；Martin边界。读者对象：数学、物理专业的研究生、老师和相关的科研人员。