随机过程高级教程(英文版)
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图灵原版数学统计学系列

随机过程高级教程(英文版)

Samuel Karlin , Howard M.Taylor (作者)
终止销售
本书是《随机过程初级教程》的姊妹篇,涉及范围十分广泛,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、独立同分布随机变量部分和的波动理论、排队过程等. 每章末都有很丰富的习题,并附有代表性的参考书目,非常便于进一步学习.
本书适合从事各领域随机过程研究和应用的读者阅读和参考.
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出版信息

  • 书  名随机过程高级教程(英文版)
  • 系列书名图灵原版数学统计学系列
  • 执行编辑关于本书的内容有任何问题,请联系 傅志红
  • 出版日期2008-12-08
  • 书  号978-7-115-19181-6
  • 定  价89.00 元
  • 页  数560
  • 开  本16开
  • 出版状态终止销售
  • 原书名A Second Course in Stochastic Processes
  • 原书号978-0-12-398650-4

同系列书

目录

Preface to A First Course x
Preface to First Edition  xv
Contents of A First Course  xvii
Chapter 10
ALGEBRAIC METHODS IN MARKOV CHAINS
1. Prelimmanes  
2. Relations of Eigenvalues and Recurrence Classes  3
3. Periodic Classes  6
4. Special Computational Methods in Markov Chains 10
5. Examples  14
6. Applications to Coin Tossing  18
Elementary Problems  23
Problems  25
Notes  30
References  30
Chapter I1
RATIO THEOREMS OF TRANsITIoN PROBABILITIES AND APPLIcATIoNS
1 Taboo Probabdiues  31
2. Ratio Theorems  33
3. Existence of Generalized Stationary Distributions  37
4. Interpretation of Generalized Stationary Distributions  42
5. Regular, Superregular, and Subregular Sequences for Markov Chains  44
6. Stopping Rule Problems  50
Elementary Problems  65
Problems  65
Notes  70
References  71
Chapter 12
SUMS OF INDEPENDENT RANDOM VARIABLES AS A MARKOV CHAIN
1. Recurrence Properties of Sums of Independent Random Variables  72
2. Local Limit Theorems  -. -.  76
3. Right Regular Sequences for the Markov Chain {S.} 83
4. The Discrete Renewal Theorem  93
Elementary Problems  95  Problems 96
Notes  99
References  99
Chapter 13
ORDER STATISTICS, POISSON PROCESSES, AND
APPLICATIONS
1. Order Statistics and Their Relation to Poisson Processes  100
2. The Ballot Problem  . 107
3. Empirical Distribution Functions and Order Statistics 113
4. Some Limit Distributions for Empirical Distribution Functions  119
Elementary Problems  124
Problems  125
Notes 137
References  137
Chapter 14
CONTINUOUS TIME MARKOV CHAINS
1. Differentiability Properties of Transition Probabilities  138
2. Conservative Processes and the Forward and Backward Differential Equations  143
3. Construction of a Continuous Time Markov Chain from Its Infinitesimal Parameters  145
4. Strong Markov Property  149
Problems  152
Notes  156
References  156
Chapter 15
DIFFUSION PROCESSES
1. General Description  157
2. Examples of Diffusion  169
3. Differential Equations Associated with Certain Functionals  191
4. Some Concrete Cases of the Functional Calculations 205
5. The Nature of Backward and Forward Equations and Calculation of Stationary Measures 213
6. Boundary Classification for Regular Diffusion Processes 226
7. Some Further Characterization of Boundary Behavior  242
8. Some Constructions of Boundary Behavior of Diffusion Processes  251
9. Conditioned Diffusion Processes  261
10. Some Natural Diffusion Models with Killing 272
11. Semigroup Formulation of Continuous Time Markov Processes  285
12. Further Topics in the Semigroup Theory of Markov Processes and Applications to Diffusions  305
13. The Spectral Representation of the Transition Density for a Diffusion  330
14. The Concept of Stochastic Differential Equations 340
15. Some Stochastic Differential Equation Models 358
16. A Preview of Stochastic Differential Equations and
Stochastic Integrals  368
Elementary Problems  377
Problems  382
Notes  395
References  395
Chapter 16
COMPOUNDING STOCHASTIC PROCESSES
1. Multidimensional Homogeneous Poisson Processes 398
2. An Application of Multidimensional Poisson Processes to Astronomy  404
3. Immigration and Population Growth 405
4. Stochastic Models of Mutation and Growth  408
5. One-Dimensional Geometric Population Growth  413
6. Stochastic Population Growth Model in Space and Time  416
7. Deterministic Population Growth with Age Distribution  419
8. A Discrete Aging Model  425
9. Compound Poisson Processes  426
Elementary Problems  441
Problems  41
Notes  450
References  450
Chapter 17
FLUCTUATION THEORY OF PARTIAL SUMS OF INDEPENDENT IDENTICALLY DISTRIBUTED RANDOM VARIABLES
1. The Stochastic Process of Partial Sums 451
2. An Equivalence Principle  453
3. Some Fundamental Identities of Fluctuation Theory and Direct Applications  459
4. The Important Concept of Ladder Random Variables 464
5. Proof of the Main Fluctuation Theory Identities 468
6. More Applications of Fluctuation Theory  473
Problems  484
Notes  488
References  488
Chapter 18
QUEUEING PROCESSES  
1 General Description  489
2. The Simplest Queueing Processes (M/M/l)  490
3. Some General One-Server Queueing Models 492
4. Embedded Markov Chain Method Applied to the Queueing Model (M/GI/l)  497
5. Exponential.Service Tim~ (G/M/1) 504
6. Gamma Amval Dtstnbutlon and Generalizations (Ek/M/1)  506
7. Exponential Service with s Servers (GI/M/s)  511
8. The Virtual Waiting Time and the Busy Period 513
Problems  519
Notes  23
References  525
MISCELLANEOUS PROBLEMS  527
Index  539
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