随机过程高级教程

Chapter 10　ALGEBRAIC METHODS IN MARKOV CHAINS

1.Preliminaria

2.Relations of Eigenvalues and Recurrence Claum

3.Periodic Classes

4.Special Computational Methods in Markov Chains

5.Examples

6.Applications to Coin Tomin

Elementary Problems

Problermt

Nores

References

Chapter 11 RATIO THEoREMS oF TRANSITl0N PROBABILITIES AND APPLICATl0NS

1.Taboo Probabilities

2.RatioTheorems

3.Existence of Generalized Stationary Distributions

4.Interpretation of Generalized Stationary Distributions

5.Regular， Superregular， and Subregular Sequences for　Markov Chains

6.Stopping Rule Problems

Elementary Problems

Problems

Notes

References

Chapter 12　SUMS OF INDEPENDENT RANDOM VARIABLES AS A MARKOV CHAIN

1.Recurrence Properties of Sums of Independent Random Variables

2.Local Limit Theorems

3.Right Regular Sequences for the Markov Chain

4.The Discrete Renewal Theorem

Elementary Problems

Problems

Notes

References

Chapter 13　ORDER STATISTICS， POISSON PROCESSES， AND

APPLICATIONS

1.Order Statistics and Their Relation to Poisson Processes

2.The Ballot Problem

3.Empirical Distribution Functions

4.Some Limit Distributions for Empirical Distribution Functions

Elementary Problems

Problems

Notes

References

Chapter 14 CONTINUOUS TIME MARKOV CHAINS

1. Differentiability Properties of Transition Probabilities

2. Conservative Processes and the Forward and Backward Differential Equations

3. Construction of a Continuous Time Markov Chain from Its Infinitesimal Parameters

4. Strong Markov Property

Problems

Notes

References

Chapter 15 DIFFUSION PROCESSES ..

1. General Description

2. Examples of Diffusion

3. Differential Equations Associated with Certain Functionals

4. Some Concrete Cases of the Functional Calculations

5. The Nature of Backward and Forward Equations and Calculation of Stationary Measures

6. Boundary Classification for Regular Diffusion Processes

7. Some Further Characterization of Boundary Behavior

8. Some Constructions of Boundary Behavior of Diffusion Processes

9. Conditioned Diffusion Processes

10. Some Natural Diffusion Models with Killing

11. Semigroup Formulation of Continuous Time Markov Processes

12. Further Topics in the Semigroup Theory of Markov Processes and Applications to Diffusions

13. The Spectral Representation of the Transition Density for a Diffusion

14. The Concept of Stochastic Differential Equations

15. Some Stochastic Differential Equation Models

16. A Preview of Stochastic Differential Equations and Stochastic Integrals

Elementary Problems

Problems

Notes

References

Chapter 16 COMPOUNDING STOCHASTIC PROCESSES

1. Multidimensional Homogeneous Poisson Processes

2. An Application of Multidimensional Poisson Processes to Astronomy

3. Immigration and Population Growth

4. Stochastic Models of Mutation and Growth

5. One-Dimensional Geometric Population Growth

6. Stochastic Population Growth Model in Space and Time

7. Deterministic Population Growth with Age Distribution

8. A Discrete Aging Model

9. Compound Poisson Processes

Elementary Problems

Problems

Notes

References

Chapter 17 FLUCTUATION THEORY OF PARTIAL SUMS OF INDEPENDENT IDENTICALLY DISTRIBUTED RANDOM VARIABLES

1. The Stochastic Process of Partial Sums

2. An Equivalence Principle

3. Some Fundamental Identities of Fluctuation Theory and Direct Applications

4. The Important Concept of Ladder Random Variables

5. Proof of the Main Fluctuation Theory Identities

6. More Applications of Fluctuation Theory

Problems

Notes

References

Chapter 18 QUEUEING PROCESSES

1. General Description

2. The Simplest Queueing Processes(M/M/l)

3. Some General One-Server Queueing Models

4. Embedded Markov Chain Method Applied to the Queueing Model(M/GI/l)

5. Exponential Service Times(G/M/1)

6. Gamma Amval Dtstnbutlon and Generalizations(Ek/M/1)

7. Exponential Service with s Servers(GI/M/s)

8. The Virtual Waiting Time and the Busy Period

Problems

Notes

References

MISCELLANEOUS PROBLEMS

Index

本书是人民邮电出版社影印和翻译出版的《随机过程初级教程》的姊妹篇，内容包括马尔可夫链的代数方法、转移概率的比定理及应用、连续时间马尔可夫链、扩散过程、复合随机过程、独立同分布随机变理部分和波动理论、排队过程等很多主题。本书将理论与应用有机地结合在一起，取得了完美的平衡。
　　本书适用而广，可供数学、物理学、生物学、社会学、管理学和其他工程领域的理论研究者和实践者学习。

《随机过程高级教程(英文版)》将理论与应用有机地结合在一起，取得了完美的平衡。《随机过程高级教程(英文版)》适用而广，可供数学、物理学、生物学、社会学、管理学和其他工程领域的理论研究者和实践者学习。