标题：应用随机过程——概率模型导论
基本信息
【作者】         [美] Sheldon M. Ross         
【编辑】         明永玲 
【ISBN】         978-7-115-24707-0         
【日期】         2011-2 
【版次】         1         
【印次】         1 
【页数】         784页         
【字数】         1053千字 
【开本】         16         
【定价】         99元
内容简介
本书叙述深入浅出，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，本书有约700道习题，其中带星号的习题还提供了解答。
本书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。
目录
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