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。
目錄：
1 Introduction to Probability Theory 11.1 Introduction 11.2 Sample Space and Events 11.3 Probabilities Defined on Events 31.4 Conditional Probabilities 61.5 Independent Events 91.6 Bayes’ Formula 111.7 Probability Is a Continuous Event Function 14Exercises 15References 212 Random Variables 232.1 Random Variables 232.2 Discrete Random Variables 272.2.1 The Bernoulli Random Variable 282.2.2 The Binomial Random Variable 282.2.3 The Geometric Random Variable 302.2.4 The Poisson Random Variable 312.3 Continuous Random Variables 322.3.1 The Uniform Random Variable 332.3.2 Exponential Random Variables 352.3.3 Gamma Random Variables 352.3.4 Normal Random Variables 352.4 Expectation of a Random Variable 372.4.1 The Discrete Case 372.4.2 The Continuous Case 392.4.3 Expectation of a Function of a Random Variable 412.5 Jointly Distributed Random Variables 442.5.1 Joint Distribution Functions 442.5.2 Independent Random Variables 492.5.3 Covariance and Variance of Sums of Random Variables 50 Properties of Covariance 522.5.4 Joint Probability Distribution of Functions of Random Variables 592.6 Moment Generating Functions 622.6.1 The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population 702.7 Limit Theorems 732.8 Proof of the Strong Law of Large Numbers 792.9 Stochastic Processes 84Exercises 86References 993 Conditional Probability and Conditional Expectation 1013.1 Introduction 1013.2 The Discrete Case 1013.3 The Continuous Case 1043.4 Computing Expectations by Conditioning 1083.4.1 Computing Variances by Conditioning 1203.5 Computing Probabilities by Conditioning 1243.6 Some Applications 1433.6.1 A List Model 1433.6.2 A Random Graph 1453.6.3 Uniform Priors， Polya’s Urn Model， and Bose?CEinstein Statistics 1523.6.4 Mean Time for Patterns 1563.6.5 The k-Record Values of Discrete Random Variables 1593.6.6 Left Skip Free Random Walks 1623.7 An Identity for Compound Random Variables 1683.7.1 Poisson Compounding Distribution 1713.7.2 Binomial Compounding Distribution 1723.7.3 A Compounding Distribution Related to the Negative Binomial 173Exercises 1744 Markov Chains 1934.1 Introduction 1934.2 Chapman?CKolmogorov Equations 1974.3 Classification of States 2054.4 Long-Run Proportions and Limiting Probabilities 2154.4.1 Limiting Probabilities 2324.5 Some Applications 2334.5.1 The Gambler’s Ruin Problem 2334.5.2 A Model for Algorithmic Efficiency 2374.5.3 Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem 2394.6 Mean Time Spent in Transient States 2454.7 Branching Processes 2475.2.2 Properties of the Exponential Distribution 2954.8 Time Reversible Markov Chains 2514.9 Markov Chain Monte Carlo Methods 2614.10 Markov Decision Processes 2654.11 Hidden Markov Chains 2694.11.1 Predicting the States 273Exercises 275References 2915 The Exponential Distribution and the Poisson Process 2935.1 Introduction 2935.2 The Exponential Distribution 2935.2.1 Definition 2935.2.2 Properties of the Exponential Distribution 2955.2.3 Further Properties of the Exponential Distribution 3025.2.4 Convolutions of Exponential Random Variables 3095.2.5 The Dirichlet Distribution 3135.3 The Poisson Process 3145.3.1 Counting Processes 3145.3.2 Definition of the Poisson Process 3165.3.3 Further Properties of Poisson Processes 3205.3.4 Conditional Distribution of the Arrival Times 3265.3.5 Estimating Software Reliability 3365.4 Generalizations of the Poisson Process 3395.4.1 Nonhomogeneous Poisson Process 3395.4.2 Compound Poisson Process 346Examples of Compound Poisson Processes 3465.4.3 Conditional or Mixed Poisson Processes 3515.5 Random Intensity Functions and Hawkes Processes 353Exercises 357References 3746 Continuous-Time Markov Chains 3756.1 Introduction 3756.2 Continuous-Time Markov Chains 3756.3 Birth and Death Processes 3776.4 The Transition Probability Function Pi j (t) 3846.5 Limiting Probabilities 3946.6 Time Reversibility 4016.7 The Reversed Chain 4096.8 Uniformization 4146.9 Computing the Transition Probabilities 418Exercises 420References 4297 Renewal Theory and Its Applications 4317.1 Introduction 4317.2 Distribution of N (t) 4327.3 Limit Theorems and Their Applications 4367.4 Renewal Reward Processes 4507.5 Regenerative Processes 4617.5.1 Alternating Renewal Processes 4647.6 Semi-Markov Processes 4707.7 The Inspection Paradox 4737.8 Computing the Renewal Function 4767.9 Applications to Patterns 4797.9.1 Patterns of Discrete Random Variables 4797.9.2 The Expected Time to a Maximal Run of Distinct Values 4867.9.3 Increasing Runs of Continuous Random Variables 4887.10 The Insurance Ruin Problem 489Exercises 495References 5068 Queueing Theory 5078.1 Introduction 5078.2 Preliminaries 5088.2.1 Cost Equations 5088.2.2 Steady-State Probabilities 5098.3 Exponential Models 5128.3.1 A Single-Server Exponential Queueing System 5128.3.2 A Single-Server Exponential Queueing System Having Finite Capacity 5228.3.3 Birth and Death Queueing Models 5278.3.4 A Shoe Shine Shop 5348.3.5 Queueing Systems with Bulk Service 5368.4 Network of Queues 5408.4.1 Open Systems 5408.4.2 Closed Systems 5448.5 The System M/G/1 5498.5.1 Preliminaries: Work and Another Cost Identity 5498.5.2 Application of Work to M/G/1 5508.5.3 Busy Periods 5528.6 Variations on the M/G/1 5548.6.1 The M/G/1 with Random-Sized Batch Arrivals 5548.6.2 Priority Queues 5558.6.3 An M/G/1 Optimization Example 5588.6.4 The M/G/1 Queue with Server Breakdown 5628.7 The Model G/M/1 5658.7.1 The G/M/1 Busy and Idle Periods 5698.8 A Finite Source Model 5708.9 Multiserver Queues 5738.9.1 Erlang’s Loss System 5748.9.2 The M/M/k Queue 5758.9.3 The G/M/k Queue 5758.9.4 The M/G/k Queue 577Exercises 5789 Reliability Theory 5919.1 Introduction 5919.2 Structure Functions 5919.2.1 Minimal Path and Minimal Cut Sets 5949.3 Reliability of Systems of Independent Components 5979.4 Bounds on the Reliability Function 6019.4.1 Method of Inclusion and Exclusion 6029.4.2 Second Method for Obtaining Bounds on r(p) 6109.5 System Life as a Function of Component Lives 6139.6 Expected System Lifetime 6209.6.1 An Upper Bound on the Expected Life of a Parallel System 6239.7 Systems with Repair 6259.7.1 A Series Model with Suspended Animation 630Exercises 632References 63810 Brownian Motion and Stationary Processes 63910.1 Brownian Motion 63910.2 Hitting Times， Maximum Variable， and the Gambler’s Ruin Problem 64310.3 Variations on Brownian Motion 64410.3.1 Brownian Motion with Drift 64410.3.2 Geometric Brownian Motion 64410.4 Pricing Stock Options 64610.4.1 An Example in Options Pricing 64610.4.2 The Arbitrage Theorem 64810.4.3 The Black?CScholes Option Pricing Formula 65110.5 The Maximum of Brownian Motion with Drift 65610.6 White Noise 66110.7 Gaussian Processes 66310.8 Stationary and Weakly Stationary Processes 66510.9 Harmonic Analysis of Weakly Stationary Processes 670Exercises 672References 67711 Simulation 67911.1 Introduction 67911.2 General Techniques for Simulating Continuous Random Variables 68311.2.1 The Inverse Transformation Method 68311.2.2 The Rejection Method 68411.2.3 The Hazard Rate Method 68811.3 Special Techniques for Simulating Continuous Random Variables 69111.3.1 The Normal Distribution 69111.3.2 The Gamma Distribution 69411.3.3 The Chi-Squared Distribution 69511.3.4 The Beta (n， m) Distribution 69511.3.5 The Exponential Distribution—The Von Neumann Algorithm 69611.4 Simulating from Discrete Distributions 69811.4.1 The Alias Method 70111.5 Stochastic Processes 70511.5.1 Simulating a Nonhomogeneous Poisson Process 70611.5.2 Simulating a Two-Dimensional Poisson Process 71211.6 Variance Reduction Techniques 71511.6.1 Use of Antithetic Variables 71611.6.2 Variance Reduction by Conditioning 71911.6.3 Control Variates 72311.6.4 Importance Sampling 72511.7 Determining the Number of Runs 73011.8 Generating from the Stationary Distribution of a Markov Chain 73111.8.1 Coupling from the Past 73111.8.2 Another Approach 733Exercises 734References 74112 Coupling 74312.1 A Brief Introduction 74312.2 Coupling and Stochastic Order Relations 74312.3 Stochastic Ordering of Stochastic Processes 74612.4 Maximum Couplings， Total Variation Distance， and the Coupling Identity 74912.5 Applications of the Coupling Identity 75212.5.1 Applications to Markov Chains 75212.6 Coupling and Stochastic Optimization 75812.7 Chen?CStein Poisson Approximation Bounds 762Exercises 769Solutions to Starred Exercises 773Index 817
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