本书包括了马尔可夫链、更新过程、鞅过程、布朗运动、分支过程和平稳过程等很多主题，涵盖了应用随机过程中最重要、联系最紧密的过程类型。本书将理论与应用有机地结合在一起，既能使学习纯数学的学生知道随机过程的多种应用，增加学习的兴趣，也能使从事应用的学生认识到基础理论在实际工作中的重要性。

本书原版自出版以来一直深受好评，已重印十多次，被斯坦福大学、华盛顿大学、加州大学等众多学校指定为教材或主要参考书。

本书系统论述随机过程的基本理论和方法，理论与实际应用并重。书中主要内容有：马尔可夫链、连续时间马尔可夫链、更新过程、鞅论、布朗运动、分支过程和平稳随机过程。本书涉及范围十分广泛，含有丰富的背景知识，深入浅出，不需要测度论作为预备知识。

本书可作为高等学校本科生和研究生的教材，也可作为工程技术人员的参考书。

Chapter 1　ELEMENTS OF STOCHASTIC PROCESSES

 1.Review of Basic Terminology and Properties of Random Variables and Distribution Functions

 2.Two Simple Examples of Stochastic Processes

 3.Classification of General Stochastic Processes

 4.Defining a Stochastic Process

Elementary Problems

Problems

Notes

References

Chapter 2　MARKOV CHAINS

 1.Definitions

 2.Examples of Markov Chains

 3.Transition Probability Matrices of a Markov Chain

 4.Classification of States of a Markov Chain

 5.Recurrence

 6.Examples of Recurrent Markov Chmns

 7.More on Recurrence

Elementary Problems

Problems

Notes

References

Chapter 3　THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND PLICATIONS

 1.Discrete Renewal Equation

 2.Proof of Theorem  1.1

 3.Absorption Probabilities

 4.Criteria for Recurrence

 5.A Queueing Example

 6.Another Queueing Model

 7.Random Walk

Elementary Problems

Problems

Notes

Reference

Chapter 4　CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS

 1.General Pure Birth Processes and Poisson Processes

 2.More about Poisson Processes

 3.A Counter Model

 4.Birth and Death Processes

 5.Differential Equations of Birth and Death Processes

 6.Examples of Birth and Death Processes

 7.Birth and Death Processes with Absorbing States

 8.Finite State Continuous Time Markov Chains

Elementary Problems

Problems

Notes

Reference

Chapter 5　RENEWAL PROCESSES

 1.Definition of a Renewal Process and Related Concepts

 2.Some Examples of Renewal Processes

 3.More on Some Special Renewal Processes

 4.Renewal Equations and the Elementary Renewal Theorem

 5.The Renewal Theorem

 6.Applications of the Renewal Theorem

 7.Generalizations and Variations on Renewal Processes

 8.More Elaborate Applications of Renewal Theory

 9.Superposition of Renewal Processes

Elementary Problems

Problems

Reference

Chapter 6　MARTINGALES

 1.Preliminary Definitions and Examples

 2.Supermartingales and Submartingales

 3.The Optional Sampling Theorem

 4.Some Applications of the Optional Sampling Theorem

 5.Martingale Convergence Theorems

 6.Applications and Extensions of the Martingale Convergence Theorems

 7.Martingales with Respect to σ-Fields

 8.Other Martingales

Elementary Problems

Problems

Notes

References

Chapter 7　BROWNIAN MOTION

 1.Background Material

 2.Joint Probabilities for Brownian　Motion

 3.Continuity of Paths and the Maximum Variables

 4.Variations and Extensions

 5.Computing Some Functionals of Brownian Motion by Martingale Methods

 6.Multidimensional Brownian Motion

 7.Brownian Paths

Elementary Problems

Problems

Notes

References

Chapter 8　BRANCHING PROCESSES

 1.Discrete Time Branching Processes

 2.Generating Function Relations for Branching Processes

 3.Extinction Probabilities

 4.Examples

 5.Two-Type Branching Processes

 6.Multi-Type Branching Processes

 7.Continuous Time Branching Processes

 8.Extinction Probabilities for Continuous Time Branching Processes

 9.Limit Theorems for Continuous Time Branching Processes

 10.Two-Type Continuous Time Branching Process

 11.Branching Processes with General Variable Lifetime

Elementary Problems

Problems

Notes

Reference

Chapter 9　STATIONARY PROCESSES

 1.Definitions and Examples

 2.Mean Square Distance

 3.Mean Square Error Prediction

 4.Prediction of Covariance Stationary Processes

 5.Ergodic Theory and Stationary Processes

 6.Applications of Ergodic Theory

 7.Spectral Analysis of Covariance Stationary Processes

 8.Gaussian Systems

 9.Stationary Point Processes

 10.The Level-Crossing Problem

Elementary Problems

Problems

Notes

References

Appendix　REVIEW OF MATRIX ANALYSIS

 1.The Spectral Theorem

 2.The Frobenius Theory of Positive Matrices

Index