应用随机过程：概率模型导论（英文版·第12版）

作者: [美] 谢尔登·M.罗斯

出版社: 人民邮电出版社

出版时间: 2021-06

版次: 2

ISBN: 9787115565143

定价: 179.80

装帧: 平装

开本: 其他

纸张: 胶版纸

页数: 825页

字数: 840千字

分类: 自然科学

8人买过

本书是一部经典的随机过程著作，叙述深入浅出、涉及面广。主要内容有随机变量、条件期望、马尔可夫链、指数分布、泊松过程、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。第12版几乎各章都有新的内容，也新增了例子和习题，其中的变化是增加了讲解耦合方法的第12章，讲述了这种方法在分析随机系统时的作用。还值得一提的是，第5章介绍了一种可以适用于平稳和非平稳泊松过程的获取结果的新方法。本书配有上百道习题，其中带星号的习题还提供了解答。谢尔登·M.罗斯（Sheldon M. Ross）

国际知名概率与统计学家，南加州大学工业与系统工程系的教授。1968年博士毕业于斯坦福大学统计系，曾在加州大学伯克利分校任教多年。他是国际数理统计协会会士、运筹学与管理学研究协会（INFORMS）会士、美国洪堡资深科学家奖获得者。罗斯教授著述颇丰，他的多本畅销数学和统计教材均产生了世界性的影响，如《概率论基础教程》《随机过程》《统计模拟》等。 1 Introduction to Probability Theory 1

1.1　Introduction　1

1.2　Sample Space and Events　1

1.3　Probabilities Defined on Events　3

1.4　Conditional Probabilities　6

1.5　Independent Events　9

1.6　Bayes’ Formula　11

1.7　Probability Is a Continuous Event Function　14

Exercises　15

References　21

2　Random Variables　23

2.1　Random Variables　23

2.2　Discrete Random Variables　27

2.2.1　The Bernoulli Random Variable　28

2.2.2　The Binomial Random Variable　28

2.2.3　The Geometric Random Variable　30

2.2.4　The Poisson Random Variable　31

2.3　Continuous Random Variables　32

2.3.1　The Uniform Random Variable　33

2.3.2　Exponential Random Variables　35

2.3.3　Gamma Random Variables　35

2.3.4　Normal Random Variables　35

2.4　Expectation of a Random Variable　37

2.4.1　The Discrete Case　37

2.4.2　The Continuous Case　39

2.4.3　Expectation of a Function of a Random Variable　41

2.5　Jointly Distributed Random Variables　44

2.5.1　Joint Distribution Functions　44

2.5.2　Independent Random Variables　49

2.5.3　Covariance and Variance of Sums of Random Variables 50 Properties of Covariance　52

2.5.4　Joint Probability Distribution of Functions of Random Variables　59

2.6　Moment Generating Functions　62

2.6.1　The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population　70

2.7　Limit Theorems　73

2.8　Proof of the Strong Law of Large Numbers　79

2.9　Stochastic Processes　84

Exercises　86

References　99

3　Conditional Probability and Conditional Expectation　101

3.1　Introduction　101

3.2　The Discrete Case　101

3.3　The Continuous Case　104

3.4　Computing Expectations by Conditioning　108

3.4.1　Computing Variances by Conditioning　120

3.5　Computing Probabilities by Conditioning　124

3.6　Some Applications　143

3.6.1　A List Model　143

3.6.2　A Random Graph　145

3.6.3　Uniform Priors, Polya’s Urn Model, and Bose?CEinstein Statistics　152

3.6.4　Mean Time for Patterns　156

3.6.5　The k-Record Values of Discrete Random Variables　159

3.6.6　Left Skip Free Random Walks　162

3.7　An Identity for Compound Random Variables　168

3.7.1　Poisson Compounding Distribution　171

3.7.2　Binomial Compounding Distribution　172

3.7.3　A Compounding Distribution Related to the Negative Binomial　173

Exercises　174

4　Markov Chains　193

4.1　Introduction　193

4.2　Chapman?CKolmogorov Equations　197

4.3　Classification of States　205

4.4　Long-Run Proportions and Limiting Probabilities　215

4.4.1　Limiting Probabilities　232

4.5　Some Applications　233

4.5.1　The Gambler’s Ruin Problem　233

4.5.2　A Model for Algorithmic Efficiency　237

4.5.3　Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem　239

4.6　Mean Time Spent in Transient States　245

4.7　Branching Processes 2475.2.2 Properties of the Exponential Distribution　295

4.8　Time Reversible Markov Chains　251

4.9　Markov Chain Monte Carlo Methods　261

4.10　Markov Decision Processes　265

4.11　Hidden Markov Chains　269

4.11.1　Predicting the States　273

Exercises　275

References　291

5　The Exponential Distribution and the Poisson Process　293

5.1　Introduction　293

5.2　The Exponential Distribution　293

5.2.1　Definition　293

5.2.2　Properties of the Exponential Distribution　295

5.2.3　Further Properties of the Exponential Distribution　302

5.2.4　Convolutions of Exponential Random Variables　309

5.2.5　The Dirichlet Distribution　313

5.3　The Poisson Process　314

5.3.1　Counting Processes　314

5.3.2　Definition of the Poisson Process　316

5.3.3　Further Properties of Poisson Processes　320

5.3.4　Conditional Distribution of the Arrival Times　326

5.3.5　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

Examples　of Compound Poisson Processes　346

5.4.3　Conditional or Mixed Poisson Processes　351

5.5　Random Intensity Functions and Hawkes Processes　353

Exercises　357

References　374

6　Continuous-Time Markov Chains　375

6.1　Introduction　375

6.2　Continuous-Time Markov Chains　375

6.3　Birth and Death Processes　377

6.4　The Transition Probability Function Pi j (t)　384

6.5　Limiting Probabilities　394

6.6　Time Reversibility　401

6.7　The Reversed Chain　409

6.8　Uniformization　414

6.9　Computing the Transition Probabilities　418

Exercises　420

References　429

7　Renewal Theory and Its Applications　431

7.1　Introduction　431

7.2　Distribution of N (t)　432

7.3　Limit Theorems and Their Applications　436

7.4　Renewal Reward Processes　450

7.5　Regenerative Processes　461

7.5.1　Alternating Renewal Processes　464

7.6　Semi-Markov Processes　470

7.7　The Inspection Paradox　473

7.8　Computing the Renewal Function　476

7.9　Applications to Patterns　479

7.9.1　Patterns of Discrete Random Variables　479

7.9.2　The Expected Time to a Maximal Run of Distinct Values　486

7.9.3　Increasing Runs of Continuous Random Variables　488

7.10　The Insurance Ruin Problem　489

Exercises　495

References　506

8　Queueing Theory　507

8.1　Introduction　507

8.2　Preliminaries　508

8.2.1　Cost Equations　508

8.2.2　Steady-State Probabilities　509

8.3　Exponential Models　512

8.3.1　A Single-Server Exponential Queueing System　512

8.3.2　A Single-Server Exponential Queueing System Having Finite Capacity　522

8.3.3　Birth and Death Queueing Models　527

8.3.4　A Shoe Shine Shop　534

8.3.5　Queueing Systems with Bulk Service　536

8.4　Network of Queues　540

8.4.1　Open Systems　540

8.4.2　Closed Systems　544

8.5　The System M/G/1　549

8.5.1　Preliminaries: Work and Another Cost Identity　549

8.5.2　Application of Work to M/G/1　550

8.5.3　Busy Periods　552

8.6　Variations on the M/G/1　554

8.6.1　The M/G/1 with Random-Sized Batch Arrivals　554

8.6.2　Priority Queues　555

8.6.3　An M/G/1 Optimization Example　558

8.6.4　The M/G/1 Queue with Server Breakdown　562

8.7　The Model G/M/1　565

8.7.1　The G/M/1 Busy and Idle Periods　569

8.8　A Finite Source Model　570

8.9　Multiserver Queues　573

8.9.1　Erlang’s Loss System　574

8.9.2　The M/M/k Queue　575

8.9.3　The G/M/k Queue　575

8.9.4　The M/G/k Queue　577

Exercises　578

9　Reliability Theory　591

9.1　Introduction　591

9.2　Structure Functions　591

9.2.1　Minimal Path and Minimal Cut Sets　594

9.3　Reliability of Systems of Independent Components　597

9.4　Bounds on the Reliability Function　601

9.4.1　Method of Inclusion and Exclusion　602

9.4.2　Second Method for Obtaining Bounds on r(p)　610

9.5　System Life as a Function of Component Lives　613

9.6　Expected System Lifetime　620

9.6.1　An Upper Bound on the Expected Life of a Parallel System　623

9.7　Systems with Repair　625

9.7.1　A Series Model with Suspended Animation　630

Exercises　632

References　638

10　Brownian Motion and Stationary Processes　639

10.1　Brownian Motion　639

10.2　Hitting Times, Maximum Variable, and the Gambler’s Ruin Problem　643

10.3　Variations on Brownian Motion　644

10.3.1　Brownian Motion with Drift　644

10.3.2　Geometric Brownian Motion　644

10.4　Pricing Stock Options　646

10.4.1　An Example in Options Pricing　646

10.4.2　The Arbitrage Theorem　648

10.4.3　The Black?CScholes Option Pricing Formula　651

10.5　The Maximum of Brownian Motion with Drift　656

10.6　White Noise　661

10.7　Gaussian Processes　663

10.8　Stationary and Weakly Stationary Processes　665

10.9　Harmonic Analysis of Weakly Stationary Processes　670

Exercises　672

References　677

11　Simulation　679

11.1　Introduction　679

11.2　General Techniques for Simulating Continuous Random Variables　683

11.2.1　The Inverse Transformation Method　683

11.2.2　The Rejection Method　684

11.2.3　The Hazard Rate Method　688

11.3　Special Techniques for Simulating Continuous Random Variables　691

11.3.1　The Normal Distribution　691

11.3.2　The Gamma Distribution　694

11.3.3　The Chi-Squared Distribution　695

11.3.4　The Beta (n, m) Distribution　695

11.3.5　The Exponential Distribution—The Von Neumann Algorithm　696

11.4　Simulating from Discrete Distributions　698

11.4.1　The Alias Method　701

11.5　Stochastic Processes　705

11.5.1　Simulating a Nonhomogeneous Poisson Process　706

11.5.2　Simulating a Two-Dimensional Poisson Process　712

11.6　Variance Reduction Techniques　715

11.6.1　Use of Antithetic Variables　716

11.6.2　Variance Reduction by Conditioning　719

11.6.3　Control Variates　723

11.6.4　Importance Sampling　725

11.7　Determining the Number of Runs　730

11.8　Generating from the Stationary Distribution of a Markov Chain　731

11.8.1　Coupling from the Past　731

11.8.2　Another Approach　733

Exercises　734

References　741

12　Coupling　743

12.1　A Brief Introduction　743

12.2　Coupling and Stochastic Order Relations　743

12.3　Stochastic Ordering of Stochastic Processes　746

12.4　Maximum Couplings, Total Variation Distance, and the Coupling Identity　749

12.5　Applications of the Coupling Identity　752

12.5.1　Applications to Markov Chains　752

12.6　Coupling and Stochastic Optimization　758

12.7　Chen?CStein Poisson Approximation Bounds　762

Exercises　769

Solutions　to Starred Exercises　773

Index　817
内容简介:
本书是一部经典的随机过程著作，叙述深入浅出、涉及面广。主要内容有随机变量、条件期望、马尔可夫链、指数分布、泊松过程、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。第12版几乎各章都有新的内容，也新增了例子和习题，其中的变化是增加了讲解耦合方法的第12章，讲述了这种方法在分析随机系统时的作用。还值得一提的是，第5章介绍了一种可以适用于平稳和非平稳泊松过程的获取结果的新方法。本书配有上百道习题，其中带星号的习题还提供了解答。
作者简介:
谢尔登·M.罗斯（Sheldon M. Ross）

国际知名概率与统计学家，南加州大学工业与系统工程系的教授。1968年博士毕业于斯坦福大学统计系，曾在加州大学伯克利分校任教多年。他是国际数理统计协会会士、运筹学与管理学研究协会（INFORMS）会士、美国洪堡资深科学家奖获得者。罗斯教授著述颇丰，他的多本畅销数学和统计教材均产生了世界性的影响，如《概率论基础教程》《随机过程》《统计模拟》等。
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　3

1.4　Conditional Probabilities　6

1.5　Independent Events　9

1.6　Bayes’ Formula　11

1.7　Probability Is a Continuous Event Function　14

Exercises　15

References　21

2　Random Variables　23

2.1　Random Variables　23

2.2　Discrete Random Variables　27

2.2.1　The Bernoulli Random Variable　28

2.2.2　The Binomial Random Variable　28

2.2.3　The Geometric Random Variable　30

2.2.4　The Poisson Random Variable　31

2.3　Continuous Random Variables　32

2.3.1　The Uniform Random Variable　33

2.3.2　Exponential Random Variables　35

2.3.3　Gamma Random Variables　35

2.3.4　Normal Random Variables　35

2.4　Expectation of a Random Variable　37

2.4.1　The Discrete Case　37

2.4.2　The Continuous Case　39

2.4.3　Expectation of a Function of a Random Variable　41

2.5　Jointly Distributed Random Variables　44

2.5.1　Joint Distribution Functions　44

2.5.2　Independent Random Variables　49

2.5.3　Covariance and Variance of Sums of Random Variables 50 Properties of Covariance　52

2.5.4　Joint Probability Distribution of Functions of Random Variables　59

2.6　Moment Generating Functions　62

2.6.1　The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population　70

2.7　Limit Theorems　73

2.8　Proof of the Strong Law of Large Numbers　79

2.9　Stochastic Processes　84

Exercises　86

References　99

3　Conditional Probability and Conditional Expectation　101

3.1　Introduction　101

3.2　The Discrete Case　101

3.3　The Continuous Case　104

3.4　Computing Expectations by Conditioning　108

3.4.1　Computing Variances by Conditioning　120

3.5　Computing Probabilities by Conditioning　124

3.6　Some Applications　143

3.6.1　A List Model　143

3.6.2　A Random Graph　145

3.6.3　Uniform Priors, Polya’s Urn Model, and Bose?CEinstein Statistics　152

3.6.4　Mean Time for Patterns　156

3.6.5　The k-Record Values of Discrete Random Variables　159

3.6.6　Left Skip Free Random Walks　162

3.7　An Identity for Compound Random Variables　168

3.7.1　Poisson Compounding Distribution　171

3.7.2　Binomial Compounding Distribution　172

3.7.3　A Compounding Distribution Related to the Negative Binomial　173

Exercises　174

4　Markov Chains　193

4.1　Introduction　193

4.2　Chapman?CKolmogorov Equations　197

4.3　Classification of States　205

4.4　Long-Run Proportions and Limiting Probabilities　215

4.4.1　Limiting Probabilities　232

4.5　Some Applications　233

4.5.1　The Gambler’s Ruin Problem　233

4.5.2　A Model for Algorithmic Efficiency　237

4.5.3　Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem　239

4.6　Mean Time Spent in Transient States　245

4.7　Branching Processes 2475.2.2 Properties of the Exponential Distribution　295

4.8　Time Reversible Markov Chains　251

4.9　Markov Chain Monte Carlo Methods　261

4.10　Markov Decision Processes　265

4.11　Hidden Markov Chains　269

4.11.1　Predicting the States　273

Exercises　275

References　291

5　The Exponential Distribution and the Poisson Process　293

5.1　Introduction　293

5.2　The Exponential Distribution　293

5.2.1　Definition　293

5.2.2　Properties of the Exponential Distribution　295

5.2.3　Further Properties of the Exponential Distribution　302

5.2.4　Convolutions of Exponential Random Variables　309

5.2.5　The Dirichlet Distribution　313

5.3　The Poisson Process　314

5.3.1　Counting Processes　314

5.3.2　Definition of the Poisson Process　316

5.3.3　Further Properties of Poisson Processes　320

5.3.4　Conditional Distribution of the Arrival Times　326

5.3.5　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

Examples　of Compound Poisson Processes　346

5.4.3　Conditional or Mixed Poisson Processes　351

5.5　Random Intensity Functions and Hawkes Processes　353

Exercises　357

References　374

6　Continuous-Time Markov Chains　375

6.1　Introduction　375

6.2　Continuous-Time Markov Chains　375

6.3　Birth and Death Processes　377

6.4　The Transition Probability Function Pi j (t)　384

6.5　Limiting Probabilities　394

6.6　Time Reversibility　401

6.7　The Reversed Chain　409

6.8　Uniformization　414

6.9　Computing the Transition Probabilities　418

Exercises　420

References　429

7　Renewal Theory and Its Applications　431

7.1　Introduction　431

7.2　Distribution of N (t)　432

7.3　Limit Theorems and Their Applications　436

7.4　Renewal Reward Processes　450

7.5　Regenerative Processes　461

7.5.1　Alternating Renewal Processes　464

7.6　Semi-Markov Processes　470

7.7　The Inspection Paradox　473

7.8　Computing the Renewal Function　476

7.9　Applications to Patterns　479

7.9.1　Patterns of Discrete Random Variables　479

7.9.2　The Expected Time to a Maximal Run of Distinct Values　486

7.9.3　Increasing Runs of Continuous Random Variables　488

7.10　The Insurance Ruin Problem　489

Exercises　495

References　506

8　Queueing Theory　507

8.1　Introduction　507

8.2　Preliminaries　508

8.2.1　Cost Equations　508

8.2.2　Steady-State Probabilities　509

8.3　Exponential Models　512

8.3.1　A Single-Server Exponential Queueing System　512

8.3.2　A Single-Server Exponential Queueing System Having Finite Capacity　522

8.3.3　Birth and Death Queueing Models　527

8.3.4　A Shoe Shine Shop　534

8.3.5　Queueing Systems with Bulk Service　536

8.4　Network of Queues　540

8.4.1　Open Systems　540

8.4.2　Closed Systems　544

8.5　The System M/G/1　549

8.5.1　Preliminaries: Work and Another Cost Identity　549

8.5.2　Application of Work to M/G/1　550

8.5.3　Busy Periods　552

8.6　Variations on the M/G/1　554

8.6.1　The M/G/1 with Random-Sized Batch Arrivals　554

8.6.2　Priority Queues　555

8.6.3　An M/G/1 Optimization Example　558

8.6.4　The M/G/1 Queue with Server Breakdown　562

8.7　The Model G/M/1　565

8.7.1　The G/M/1 Busy and Idle Periods　569

8.8　A Finite Source Model　570

8.9　Multiserver Queues　573

8.9.1　Erlang’s Loss System　574

8.9.2　The M/M/k Queue　575

8.9.3　The G/M/k Queue　575

8.9.4　The M/G/k Queue　577

Exercises　578

9　Reliability Theory　591

9.1　Introduction　591

9.2　Structure Functions　591

9.2.1　Minimal Path and Minimal Cut Sets　594

9.3　Reliability of Systems of Independent Components　597

9.4　Bounds on the Reliability Function　601

9.4.1　Method of Inclusion and Exclusion　602

9.4.2　Second Method for Obtaining Bounds on r(p)　610

9.5　System Life as a Function of Component Lives　613

9.6　Expected System Lifetime　620

9.6.1　An Upper Bound on the Expected Life of a Parallel System　623

9.7　Systems with Repair　625

9.7.1　A Series Model with Suspended Animation　630

Exercises　632

References　638

10　Brownian Motion and Stationary Processes　639

10.1　Brownian Motion　639

10.2　Hitting Times, Maximum Variable, and the Gambler’s Ruin Problem　643

10.3　Variations on Brownian Motion　644

10.3.1　Brownian Motion with Drift　644

10.3.2　Geometric Brownian Motion　644

10.4　Pricing Stock Options　646

10.4.1　An Example in Options Pricing　646

10.4.2　The Arbitrage Theorem　648

10.4.3　The Black?CScholes Option Pricing Formula　651

10.5　The Maximum of Brownian Motion with Drift　656

10.6　White Noise　661

10.7　Gaussian Processes　663

10.8　Stationary and Weakly Stationary Processes　665

10.9　Harmonic Analysis of Weakly Stationary Processes　670

Exercises　672

References　677

11　Simulation　679

11.1　Introduction　679

11.2　General Techniques for Simulating Continuous Random Variables　683

11.2.1　The Inverse Transformation Method　683

11.2.2　The Rejection Method　684

11.2.3　The Hazard Rate Method　688

11.3　Special Techniques for Simulating Continuous Random Variables　691

11.3.1　The Normal Distribution　691

11.3.2　The Gamma Distribution　694

11.3.3　The Chi-Squared Distribution　695

11.3.4　The Beta (n, m) Distribution　695

11.3.5　The Exponential Distribution—The Von Neumann Algorithm　696

11.4　Simulating from Discrete Distributions　698

11.4.1　The Alias Method　701

11.5　Stochastic Processes　705

11.5.1　Simulating a Nonhomogeneous Poisson Process　706

11.5.2　Simulating a Two-Dimensional Poisson Process　712

11.6　Variance Reduction Techniques　715

11.6.1　Use of Antithetic Variables　716

11.6.2　Variance Reduction by Conditioning　719

11.6.3　Control Variates　723

11.6.4　Importance Sampling　725

11.7　Determining the Number of Runs　730

11.8　Generating from the Stationary Distribution of a Markov Chain　731

11.8.1　Coupling from the Past　731

11.8.2　Another Approach　733

Exercises　734

References　741

12　Coupling　743

12.1　A Brief Introduction　743

12.2　Coupling and Stochastic Order Relations　743

12.3　Stochastic Ordering of Stochastic Processes　746

12.4　Maximum Couplings, Total Variation Distance, and the Coupling Identity　749

12.5　Applications of the Coupling Identity　752

12.5.1　Applications to Markov Chains　752

12.6　Coupling and Stochastic Optimization　758

12.7　Chen?CStein Poisson Approximation Bounds　762

Exercises　769

Solutions　to Starred Exercises　773

Index　817

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应用随机过程：概率模型导论（英文版·第12版）

内容简介:

作者简介:

目录: