马尔科夫过程、布朗运动和时间对称 : 第2版

Chapter 1 Markov Ptocess

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 I

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

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. FineProperties

Exercises

3.6.Decreasing Limits

Exercises

3.7.Recurrence and Transience

Exercises

3.8.Hypothesis (B)

Exerases

Notes on Chapter 3

Chapter 4 Brownian Motion

4.1.Spatial Homogeneity

Exercises

4.2.Preliminary Properties of Brownian Motion

Exercises

4.3.Harmonic Function

Exerases

4.4.Dirichlet Problem

Exercises

4.5.Superharmonic Function and Supermartingale

Exerases

4.6.The Role of the Laplacian

Exercises

4.7. The Feynman-Kac Functional and the Schrodinger Equation

Exe工ases

Notes on Chapter 4

Chapter 5 Potential Developments

5.1 Quitting Time and Equilibrium Measure

Exercises

5.2.Some Princip les of Potential Theory

Exerases

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

8.2Branching Points

Chapter9

Application to Markov Chains

……

Chapter 10 Time Reversal

Chapter 11 h-Transforms

Chapter 12 Death and Transfiguration: A Fireside Chat

Chapter 13 Processes in Duality

Chapter 14 The Martin Boundary

Chapter 15 The Basis of Duality: A Fireside Chat

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.