概率和随机 (英文影印版)

书籍目录

Preface

Frequently Used Notation

Ⅰ Measure and Integration

1 Measurable Spaces

2 Measurable Functions

3 Measures

4 Integration

5 Transforms and Indefinite Integrals

6 Kernels and Product Spaces

Ⅱ Probability Spaces

1 Probability Spaces and Random Variables

2 Expectations

3 LP—spaces and Uniform Integrability

4 Information and Determinability

5 Independence

Ⅲ Convergence

1 Convergence of Real Sequences

2 Almost Sure Convergence

3 Convergence in Probability

4 Convergencein Lp

5 Weak Convergence

6 Laws ofLarge Numbers

7 Convergence ofSeries

8 CentraILimits

Ⅳ Conditioning

1 Conditional Expectations

2 Conditional Probabilities and Distributions

3 Conditionallndependence

4 Construction of Probability Spaces

5 Special Constructions

Ⅴ Martingales and Stochastics

1 Filtrations and Stopping Times

2 Martingales

3 Martingale Transformations and Maxima

4 Martingale Convergence

5 Martingales in Continuous Time

6 Martingale Characterizations for Wiener and Poisson

7 Standard Filtrations and Modifications of Martingales

Ⅵ Poisson Random Measures

1 Random Measures

2 Poisson Random Measures

3 Transformations

4 Additive Random Measures and Levy Processes

5 Poisson Processes

6 Poisson Integrals and Self—exciting Processes

Ⅶ Levy Processes

1 Introduction

2 Stable Processes

3 Levy Processes on Standard Settings

4 Characterizations for Wiener and Poisson

5 Ito—Levy Decomposition

6 Subordination

7 Increasing Levy Processes

Ⅷ Brownian Motion

1 Introduction

2 Hitting Times and Recurrence Times

3 Hitting Times and Running Maximum

4 Wiener and its Maximum

5 Zeros，LocaITimes

6 Excursions

7 Path Properties

8 Existence

Ⅸ Markov Processes

1 Markov Property

2 Ito Diffusions

3 Jump—Diffusions

4 Markov Systems

5 Hunt Processes

6 Potentials and Excessive Functions

7 Appendix：Stochastic Integration

Notes and Comments

Bibliography

Index

作者简介

《概率和随机》是一部兼顾理论和应用的，讲述概率和随机研究生教材。本书的风格仍然是这个系列的延续，注重随机过程的理论，但却非一味强调理论和抽象，也兼顾应用。书的前四章是有关概率论、度量和积分、概率空间、条件期望和经典极限定理；接下来的章节是有关鞅、泊松随机测度、levy过程、布朗运动和马尔科夫过程。重点强调了泊松随机测度，及其在调节布朗运动冲程和Levy跃迁和马尔科夫过程中的扮演的重要角色。每章末都有大量的例子和练习。

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