應用隨機過程概率模型導論


圖書信息
  書 名: 應用隨機過程:概率模型導論

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作 者:羅斯(SheldonM.Ross)
  出版社: 人民郵電出版社
  出版時間: 2011年2月1日
  ISBN: 9787115247070
  开本: 16开
  定價: 99.00元內容介紹
  本書是國際知名統計學家Sheldon M.Ross所著的關於基礎概率理論和隨機過程的經典教材,被加州大學伯克利分校哥倫比亞大學、普度大學、 密歇根大學、俄勒岡州立大學、華盛頓大學等衆多國外知名大學所採用。與其他隨機過程教材相比,本書非常強調實踐性,內含極其豐富的例子和習題,涵蓋了衆多學科的各種應用;作者富於啓發而又不失嚴密性的敘述方式,有助於讀者建立概率思維方式,培養對概率理論、隨機過程的直觀感覺。對那些需要將概率理論應用於精算學、運籌學、物理學、工程學、計算機科學、管理學和社會科學的讀者,本書是一本極好的教材或參考書。本書目錄
  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 21
  2 Random Variables 23
  2.1 Random Variables 23
  2.2 Discrete Random Variables 27
  2.3 Continuous Random Variables 34
  2.4 Expectation of a Random Variable 38
  2.5 Jointly Distributed Random Variables 43
  2.6 Moment Generating Functions 64
  2.7 Limit Theorems 77
  2.8 Stochastic Processes 83
  Exercises 85
  References 96
  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 105
  3.5 Computing Probabilities by Conditioning 119
  3.6 Some Applications Exercises 136
  Exercises 161
  4 Markov Chains 181
  4.1 Introduction 181
  4.2 Chapman-Kolmogorov Equations 185
  4.3 Classification of States 189
  4.4 Limiting Probabilities 200
  4.5 Some Applications 213
  4.6 Mean Time Spent in Transient States 226
  4.7 Branching Processes 228
  4.8 Time Reversible Markov Chains 232
  4.9 Markov Chain Monte Carlo Methods 243
  4.10 Markov Decision Processes 248
  Exercises 252
  References 268
  5 The Exponential Distribution and the Poisson Process 269
  5.1 Introduction 269
  5.2 The Exponential Distribution 270
  5.3 The Poisson Process 288
  5.4 Generalizations of the Poisson Process 316
  Exercises 330
  References 348
  6 Continuous-Time Markov Chains 349
  6.1 Introduction 349
  6.2 Continuous-Time Markov Chains 350
  6.3 Birth and Death Processes 352
  6.4 The Transition Probability Function Pij (t) 359
  6.5 Limiting Probabilities 368
  6.6 Time Reversibility 376
  6.7 Uniformization 384
  6.8 Computing the Transition Probabilities 388
  Exercises 390
  References 399
  7 Renewal Theory and Its Applications 401
  7.1 Introduction 401
  7.2 Distribution of N(t) 403
  7.3 Limit Theorems and Their Applications 407
  7.4 Renewal Reward Processes 416
  7.5 Regenerative Processes 425
  7.6 Semi-Markov Processes 434
  7.7 The Inspection Paradox 437
  7.8 Computing the Renewal Function 440
  7.9 Applications to Patterns 443
  7.10 The Insurance Ruin Problem 455
  Exercises 460
  References 472
  8 Queueing Theory 475
  8.1 Introduction 475
  8.2 Preliminaries 476
  8.3 Exponential Models 480
  8.4 Network of Queues 496
  8.5 The System M/G/1 507
  8.6 Variations on the M/G/1 510
  8.7 The Model G/M/1 519
  8.8 A Finite Source Model 525
  8.9 Multiserver Queues 528
  Exercises 534
  References 546
  9 Reliability Theory 547
  9.1 Introduction 547
  9.2 Structure Functions 547
  9.3 Reliability of Systems of Independent Components 554
  9.4 Bounds on the Reliability Function 559
  9.5 System Life as a Function of Component Lives 571
  9.6 Expected System Lifetime 580
  9.7 Systems with Repair 586
  Exercises 593
  References 600
  10 Brownian Motion and Stationary Processes 601
  10.1 Brownian Motion 601
  10.2 Hitting Times, Maximum Variable, and the Gambler's Ruin Problem 605
  10.3 Variations on Brownian Motion 607
  10.4 Pricing Stock Options 608
  10.5 White Noise 620
  10.6 Gaussian Processes 622
  10.7 Stationary andWeakly Stationary Processes 625
  10.8 Harmonic Analysis of Weakly Stationary Processes 630
  Exercises 633
  References 638
  11 Simulation 639
  11.1 Introduction 639
  11.2 General Techniques for Simulating Continuous Random Variables 644
  11.3 Special Techniques for Simulating Continuous Random Variables 653
  11.4 Simulating from Discrete Distributions 661
  11.5 Stochastic Processes 668
  11.6 Variance Reduction Techniques 679
  11.7 Determining the Number of Runs 696
  11.8 Coupling from the Past 696
  Exercises 699
  References 707
  Appendix: Solutions to Starred Exercises 709
  Index 749作者介紹
  國際知名統計學家,加州大學伯克利分校工業工程與運籌系教授。畢業於斯坦福大學統計系。研究領域包括:隨機模型、仿真模擬統計分析金融數學等。羅斯教授是多本暢銷數學和統計教材的作者。

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