随机过程初级教程

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 Chains

7．More On Recurrence

Elementary Problems

Problems

Notes

References

Chapter 3

THE BASIC LIMIT THEOREM 0F MARKOV CHAINS AND APPLICATl0NS

1．Discrete Renewal Equation

2．Proof of Theorem 1.1

3．Absorption Probabilities

4．Cfiteria for Recurrence

5．A Queuei~g Example

6．Another Queueing Model

7．Random Walk

Elementary Problems

Problems

Notes

Rererence

Chapter 4

CLASSICAL EXAMPLES 0F 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

References

Chapter 5

RENEWAL PROCESSES

Chapter 6

MARTINGALES

Chapter 7

BROWNIAN MOTION

Chapter 8

BRANCHING PROCESSES

Chapter 9

STATIONARY PROCESSES

REVIEW OF MATRIX ANALYSIS

Index

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。

《随机过程初级教程》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。
　　本书为英文版。