Statistics Topics Index: An Introduction to Stochastic Modeling, 3Ed

An Introduction to Stochastic Modeling, 3Ed

Courses that use this book:

[Spring 2009] Statistics 150 -- Stochastic Processes

An Introduction To Stochastic Modeling

An Introduction To Stochastic Modeling, 3ed.
Author(s): Samuel Karlin, Howard Taylor.
ISBN: 0126848874.
Year: 1998.
Publisher: Academic Press.

1 Introduction 1

1.1 Stochastic Modeling 1

1.2 Probability Review 6

1.3 The Major Discrete Distributions 24

1.4 Important Continuous Distributions 33

1.5 Some Elementary Exercises 43

1.6 Useful Functions, Integrals, And Sums 53

2 Conditional Probability And Conditional Expectation 57

2.1 The Discrete Case 57

2.2 The Dice Game Craps 64

2.3 Random Sums 70

2.4 Conditioning On A Continuous Random Variable 79

2.5 Martingales* 87

3 Markov Chains: Introduction 95

3.1 Definitions 95

3.2 Transition Probability Matrices Of A Markov Chain 100

3.3 Some Markov Chain Models 105

3.4 First Step Analysis 116

3.5 Some Special Markov Chains 135

3.6 Functionals Of Random Walks And Success Runs 151

3.7 Another Look At First Step Analysis* 169

3.8 Branching Processes* 177

3.9 Branching Processes And Generating Functions* 184

4 The Long Run Behavior Of Markov Chains 199

4.1 Regular Transition Probability Matrices 119

4.2 Examples 215

4.3 The Classification Of States 234

4.4 The Basic Limit Theorem Of Markov Chains 245

4.5 Reducible Markov Chains* 258

5 Poisson Processes 267

5.1 The Poisson Distribution And The Poisson Process, [Poisson Distribution], [Poisson Processes] 267

5.2 The Law Of Rare Events 279

5.3 Distributions Associated With The Poisson Process 290

5.4 The Uniform Distribution And Poisson Processes 297

5.5 Spatial Poisson Processes 311

5.6 Compound And Marked Poisson Processes 318

6 Continuous Time Markov Chains 333

6.1 Pure Birth Processes 333

6.2 Pure Death Processes 345

6.3 Birth And Death Processes 355

6.4 The Limiting Behavior Of Birth And Death Processes 366

6.5 Birth And Death Processes With Absorbing States 379

6.6 Finite State Continuous Time Markov Chains 394

6.7 A Poisson Process With A Markov Intensity* 408

7 Renewal Phenomena 419

7.1 Definition Of A Renewal Process And Related Concepts 419

7.2 Some Examples Of Renewal Processes 426

7.3 The Poisson Process Viewed As A Renewal Process 432

7.4 The Asymptotic Behavior Of Renewal Processes 437

7.5 Generalizations And Variations On Renewal Processes 447

7.6 Discrete Renewal Theory* 457

8 Brownian Motion And Related Processes 473

8.1 Brownian Motion And Gaussian Processes 473

8.2 The Maximum Variable And The Reflection Principle, [Reflection Principle], [Maximum Variable] 491

8.3 Variations And Extensions 498

8.4 Brownian Motion With Drift 508

8.5 The Ornstein-Uhlenbeck Process* 524

9 Queueing Systems 541

9.1 Queueing Processes 541

9.2 Poisson Arrivals, Exponential Service Times, [Exponential Service Time], [Poisson Arrivals] 547

9.3 General Service Time Distributions 558

9.4 Variations And Extensions 567

9.5 Open Acyclic Queueing Networks 581

9.6 Age 592

An Introduction to Stochastic Modeling, 3Ed

Courses that use this book:

An Introduction To Stochastic Modeling, 3ed. Author(s): Samuel Karlin, Howard Taylor. ISBN: 0126848874. Year: 1998. Publisher: Academic Press.

An Introduction To Stochastic Modeling, 3ed.
Author(s): Samuel Karlin, Howard Taylor.
ISBN: 0126848874.
Year: 1998.
Publisher: Academic Press.