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目录
Chapter 10　ALGEBRAIC METHODS IN MARKOV CHAINS
1. Prelimmanes　1　
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 11　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 {Sn}  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 Times(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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