隨機(jī)過程導(dǎo)論

內(nèi)容概要

隨機(jī)過程是對隨時間和空間變化的隨機(jī)現(xiàn)象進(jìn)行建模和分析的學(xué)科。許多年前，我們不能在現(xiàn)實問題求解中應(yīng)用隨機(jī)過程，但隨著數(shù)值方法和計算工具的快速發(fā)展，這種狀況已經(jīng)發(fā)生了變化。本書很好地將計算機(jī)的使用和隨機(jī)過程教學(xué)結(jié)合起來，采用MATLAB的計算機(jī)解題方法，使本書充滿現(xiàn)代感，又具備實用的特點。本書采用面向應(yīng)用和計算的方式，強(qiáng)調(diào)通過各種示例和習(xí)題來開發(fā)學(xué)生在隨機(jī)建模和分析中的實戰(zhàn)能力，同時將計算的任務(wù)交給計算機(jī)去完成。 本書是為那些有興趣學(xué)習(xí)隨機(jī)過程的概念、模型和計算方法的學(xué)生編寫的，是隨機(jī)過程課程的入門教材，適合管理、金融、工程、統(tǒng)計、計算機(jī)科學(xué)和應(yīng)用數(shù)學(xué)等專業(yè)的高年級本科生或低年級研究生閱讀

書籍目錄

1 Introduction 1  1.0 Overview 2  1.1 Introduction 2  1.2 Discrete Random Variables and Generating Functions 6  1.3 Continuous Random Variables and Laplace Transforms 17  1.4 Some Mathematical Background 28  Problems 37  Bibliographic Notes 42  References 43  Appendix 432 Poisson Processes 47  2.0 Overview 47  2.1 Introduction 48  2.2 Properties of Poisson Processes 51  2.3 Nonhomogeneous Poisson Processes 56  2.4 Compound Poisson Processes 72  2.5 Filtered Poisson Processes 76  2.6 Two-Dimensional and Marked Poisson Processes 80  2.1 Poisson Arrivals See Time Averages (PASTA) 83  Problems 87  Bibliographic Notes 93  References 94  Appendix 953 Renewal Processes 97  3.0 Overview 97  3.1 Introduction 98  3.2 Renewal-Type Equations 101  3.3 Excess Life, Current Life, and Total Life 107  3.4 Renewal Reward Processes 118  3.5 Limiting Theorems, Stationary and Transient Renewal Processes 128  3.6 Regenerative Processes 132  3.7 Discrete Renewal Processes 144  Problems 146  Bibliographic Notes 154  References 155  Appendix 1564 Discrete-Time Markov Chains 160  4.0 Overview 160  4.1 Introduction 161  4.2 Classification of States 167  4.3 Ergodic and Periodic Markov Chains 175  4.4 Absorbing Markov Chains 188  4.5 Markov Reward Processes 203  4.6 Reversible Discrete-Tune Markov Chains 207  Problems 212  Bibliographic Notes 225  References 226  Appendix 2275 Continuous-Time Markov Chains 238  5.0 Overview 239  5.1 Introduction 239  5.2 The Kolmogorov Differential Equations 245  5.3 The Limiting Probabilities 252  5.4 Absorbing Continuous-Time Markov Chains 256  5.S Phase-Type Distributions 264  5.6 Uniformization 273  5.7 Continuous-Time Markov Reward Processes 277  5.8 Reversible Continuous-Time Markov Chains 284  Problems 298  Bibliographic Notes 313  References 314  Appendix 3166 Markov Renewal and Semi-Regenerative Processes 321  6.0 Overview 322  6.1 Introduction 322  6.2 Markov Renewal Functions and Equations 331  6.3 Semi-Markov Processes and Related Reward Processes 339  6.4 Semi-Regenerative Processes 348  Problems 363  Bibliographic Notes 367  References 367  Appendix 3687 Brownian Motion and Other Diffusion Processes 373  7.0 Overview 373  7.1 Introduction 374  7.2 Diffusion Processes 385  7.3 Ito's Calculus and Stochastic Differential Equations 396  7.4 Multidimensional Ito's Lemma 404  7.5 Control of Systems of Stochastic Differential Equations 409  Problems 417  Bibliographic Notes 419  References 420  Appendix 421  Appendix: Getting Started with MATLAB 427  Index 436

編輯推薦

　　本書是為那些有興趣學(xué)習(xí)隨機(jī)過程的概念、模型和計算方法的學(xué)生編寫的，是隨機(jī)過程課程的入門教材，適合管理、金融、工程、統(tǒng)計、計算機(jī)科學(xué)和應(yīng)用數(shù)學(xué)等專業(yè)的高年級本科生或低年級研究生閱讀。本書采用面向應(yīng)用和計算的方式，強(qiáng)調(diào)通過各種示例和習(xí)題來開發(fā)學(xué)生在隨機(jī)建模和分析中的實戰(zhàn)能力，同時將計算的任務(wù)交給計算機(jī)去完成。			　　

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