《应用随机过程:概率模型导论(英文版·第10版)》是国际知名统计学家Sheldon M，Ross所著的关于基础概率理论和随机过程的经典教材。被加州大学伯克利分校，哥伦比亚大学、普度大学、密歇根大学、俄勒冈州立大学，华盛顿大学等众多国外知名大学所采用。

与其他随机过程教材相比《应用随机过程:概率模型导论(英文版·第10版)》非常强调实践性。内含极其丰富的例子和习题，涵盖了众多学科的各种应用。作者富于启发而又不失严密性的叙述方式，有助于使读者建立概率思维方式，培养对概率理论、随机过程的直观感觉。对那些需要将概率理论应用于精算学，运筹学，物理学，工程学，计算机科学。管理学和社会科学的读者而言，《应用随机过程:概率模型导论(英文版·第10版)》是一本极好的教材或参考书。

《应用随机过程:概率模型导论(英文版·第10版)》由Sheldon M.Ross所著，叙述深入浅出，涉及面广。主要内容有随机变量、条件概率及条件期望、离散及连续马尔可夫链、指数分布、泊松过程、布朗运动及平稳过程、更新理论及排队论等；也包括了随机过程在物理、生物、运筹、网络、遗传、经济、保险、金融及可靠性中的应用。特别是有关随机模拟的内容，给随机系统运行的模拟计算提供了有力的工具。除正文外，《应用随机过程——概率模型导论(第10版:英文版)》有约700道习题，其中带星号的习题还提供了解答。

《应用随机过程:概率模型导论(英文版·第10版)》可作为概率论与统计、计算机科学、保险学、物理学、社会科学、生命科学、管理科学与工程学等专业的随机过程基础课教材。

1 introduction to probability theory 1

 1.1 introduction 1

 1.2 sample space and events 1

 1.3 probabilities defined on events 4

 1.4 conditional probabilities 7

 1.5 independent events 10

 1.6 bayes' formula 12

 exercises 15

 references 20

2 random variables 21

 2.1 random variables 21

 2.2 discrete random variables 25

2.2.1 the bernoulli random variable 26

2.2.2 the binomial random variable 27

2.2.3 the geometric random variable 29

2.2.4 the poisson random variable 30

 2.3 continuous random variables 31

2.3.1 the uniform random variable 32

2.3.2 exponential random variables 34

2.3.3 gamma random variables 34

2.3.4 normal random variables 34

 2.4 expectation of a random variable 36

2.4.1 the discrete case 36

2.4.2 the continuous case 38

2.4.3 expectation of a function of a random variable 40

 2.5 jointly distributed random variables 44

2.5.1 joint distribution functions 44

2.5.2 independent random variables 48

2.5.3 covariance and variance of sums of random variables 50

2.5.4 joint probability distribution of functions of randomvariables 59

 2.6 moment generating functions 62

2.6.1 the joint distribution of the sample mean and sample variance from a normal population 71

 2.7 the distribution of the number of events that occur 74

 2.8 limit theorems 77

 2.9 stochastic processes 84

 exercises 86

 references 95

3 conditional probability and conditional expectation 97

 3.1 introduction 97

 3.2 the discrete case 97

 3.3 the continuous case 102

 3.4 computing expectations by conditioning 106

3.4.1 computing variances by conditioning 117

 3.5 computing probabilities by conditioning 122

 3.6 some applications 140

3.6.1 a list model 140

3.6.2 a random graph 141

3.6.3 uniform priors, polya's urn model, and bose-einstein statistics 149

3.6.4 mean time for patterns 153

3.6.5 the k-record values of discrete random variables 157

3.6.6 left skip free random walks 160

 3.7 an identity for compound random variables 166

3.7.1 poisson compounding distribution 169

3.7.2 binomial compounding distribution 171

3.7.3 a compounding distribution related to the negative binomial 172

 exercises 173

4 markov chains 191

 4.1 introduction 191

 4.2 chapman-kolmogorov equations 195

 4.3 classification of states 204

 4.4 limiting probabilities 214

 4.5 some applications 230

4.5.1 the gambler's ruin problem 230

4.5.2 a model for algorithmic efficiency 234

4.5.3 using a random walk to analyze a probabilistic algorithm for the satisfiability problem 237

 4.6 mean time spent in transient states 243

 4.7 branching processes 245

 4.8 time reversible markov chains 249

 4.9 markov chain monte carlo methods 260

 4.10 markov decision processes 265

 4.11 hidden markov chains 269

4.11.1 predicting the states 273

 exercises 275

 references 290

5 the exponential distribution and the poisson process 291

 5.1 introduction 291

 5.2 the exponential distribution 292

5.2.1 definition 292

5.2.2 properties of the exponential distribution 294

5.2.3 further properties of the exponential distribution 301

5.2.4 convolutions of exponential random variables 308

 5.3 the poisson process 312

5.3.1 counting processes 312

5.3.2 definition of the poisson process 313

5.3.3 interarrival and waiting time distributions 316

5.3.4 further properties of poisson processes 319

5.3.5 conditional distribution of the arrival times 325

5.3.6 estimating software reliability 336

 5.4 generalizations of the poisson process 339

5.4.1 nonhomogeneous poisson process 339

5.4.2 compound poisson process 346

5.4.3 conditional or mixed poisson processes 351

 exercises 354

 references 370

6 continuous-time markov chains 371

 6.1 introduction 371

 6.2 continuous-time markov chains 372

 6.3 birth and death processes 374

 6.4 the transition probability function pij (t) 381

 6.5 limiting probabilities 390

 6.6 time reversibility 397

 6.7 uniformization 406

 6.8 computing the transition probabilities 409

 exercises 412

 references 419

7 renewal theory and its applications 421

 7.1 introduction 421

 7.2 distribution of n(t) 423

 7.3 limit theorems and their applications 427

 7.4 renewal reward processes 439

 7.5 regenerative processes 447

7.5.1 alternating renewal processes 450

 7.6 semi-markov processes 457

 7.7 the inspection paradox 460

 7.8 computing the renewal function 463

 7.9 applications to patterns 466

7.9.1 patterns of discrete random variables 467

7.9.2 the expected time to a maximal run of distinct values 474

7.9.3 increasing runs of continuous random variables 476

 7.10 the insurance ruin problem 478

 exercises 484

 references 495

8 queueing theory 497

 8.1 introduction 497

 8.2 preliminaries 498

8.2.1 cost equations 499

8.2.2 steady-state probabilities 500

 8.3 exponential models 502

8.3.1 a single-server exponential queueing system 502

8.3.2 a single-server exponential queueing system having finite capacity 511

8.3.3 birth and death queueing models 517

8.3.4 a shoe shine shop 522

8.3.5 a queueing system with bulk service 524

 8.4 network of queues 527

8.4.1 open systems 527

8.4.2 closed systems 532

 8.5 the system m/g/1 538

8.5.1 preliminaries: work and another cost identity 538

8.5.2 application of work to m/g/1 539

8.5.3 busy periods 540

 8.6 variations on the m/g/1 541

8.6.1 the m/g/1 with random-sized batch arrivals 541

8.6.2 priority queues 543

8.6.3 an m/g/1 optimization example 546

8.6.4 the m/g/1 queue with server breakdown 550

 8.7 the model g/m/1 553

8.7.1 the g/m/1 busy and idle periods 558

 8.8 a finite source model 559

 8.9 multiserver queues 562

8.9.1 erlang's loss system 563

8.9.2 the m/m/k queue 564

8.9.3 the g/m/k queue 565

8.9.4 the m/g/k queue 567

 exercises 568

 references 578

9 reliability theory 579

 9.1 introduction 579

 9.2 structure functions 580

9.2.1 minimal path and minimal cut sets 582

 9.3 reliability of systems of independent components 586

 9.4 bounds on the reliability function 590

9.4.1 method of inclusion and exclusion 591

9.4.2 second method for obtaining bounds on r(p) 600

 9.5 system life as a function of component lives 602

 9.6 expected system lifetime 610

9.6.1 an upper bound on the expected life of a parallel system 614

 9.7 systems with repair 616

9.7.1 a series model with suspended animation 620

 exercises 623

 references 629

10 brownian motion and stationary processes 631

 10.1 brownian motion 631

 10.2 hitting times, maximum variable, and the gambler's ruin problem 635

 10.3 variations on brownian motion 636

10.3.1 brownian motion with drift 636

10.3.2 geometric brownian motion 636

 10.4 pricing stock options 638

10.4.1 an example in options pricing 638

10.4.2 the arbitrage theorem 640

10.4.3 the black-scholes option pricing formula 644

 10.5 white noise 649

 10.6 gaussian processes 651

 10.7 stationary and weakly stationary processes 654

 10.8 harmonic analysis of weakly stationary processes 659

 exercises 661

 references 665

11 simulation 667

 11.1 introduction 667

 11.2 general techniques for simulating continuous random variables 672

11.2.1 the inverse transformation method 672

11.2.2 the rejection method 673

11.2.3 the hazard rate method 677

 11.3 special techniques for simulating continuous random variables 680

11.3.1 the normal distribution 680

11.3.2 the gamma distribution 684

11.3.3 the chi-squared distribution 684

11.3.4 the beta (n, m) distribution 685

11.3.5 the exponential distribution-the von neumann algorithm 686

 11.4 simulating from discrete distributions 688

11.4.1 the alias method 691

 11.5 stochastic processes 696

11.5.1 simulating a nonhomogeneous poisson process 697

11.5.2 simulating a two-dimensional poisson process 703

 11.6 variance reduction techniques 706

11.6.1 use of antithetic variables 707

11.6.2 variance reduction by conditioning 710

11.6.3 control variates 715

11.6.4 importance sampling 717

 11.7 determining the number of runs 722

 11.8 generating from the stationary distribution of a markov chain 723

11.8.1 coupling from the past 723

11.8.2 another approach 725

 exercises 726

 references 734

Appendix: solutions to starred exercises 735

Index 775