《套用隨機過程：機率模型導論（英文版第11版）》是2019年3月人民郵電出版社出版的圖書，作者是[美]羅斯（Sheldon M·Ross）。
基本介紹
- 書名：套用隨機過程：機率模型導論（英文版第11版）
- 作者：[美]羅斯（Sheldon M·Ross）
- ISBN：9787115384744
- 頁數：767頁
- 定價：99元
- 出版社：人民郵電出版社
- 出版時間：2019年3月
- 裝幀：平裝
- 開本：16開
內容簡介,圖書目錄,
內容簡介
《套用隨機過程 機率模型導論》是一部經典的隨機過程著作, 敘述深入淺出、涉及面廣。 主要內容有隨機變數、條件期望、馬爾可夫鏈、指數分布、泊松過程、平穩過程、更新理論及排隊論等，也包括了隨機過程在物理、生物、運籌、網路、遺傳、經濟、保險、金融及可靠性中的套用。 特別是有關隨機模擬的內容, 給隨機系統運行的模擬計算提供了有力的工具。**新版還增加了不帶左跳的隨機徘徊和生滅排隊模型等內容。本書約有700道習題, 其中帶星號的習題還提供了解答。
《套用隨機過程 機率模型導論》可作為機率論與數理統計、計算機科學、保險學、物理學、社會科學、生命科學、管理科學與工程學等專業隨機過程基礎課教材。
圖書目錄
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 6
1.5 Independent Events 9
1.6 Bayes’ Formula 11
Exercises 14
References 19
2 Random Variables 21
2.1 Random Variables 21
2.2 Discrete Random Variables 25
2.2.1 The Bernoulli Random Variable 26
2.2.2 The Binomial Random Variable 26
2.2.3 The Geometric Random Variable 28
2.2.4 The Poisson Random Variable 29
2.3 Continuous Random Variables 30
2.3.1 The Uniform Random Variable 31
2.3.2 Exponential Random Variables 32
2.3.3 Gamma Random Variables 33
2.3.4 Normal Random Variables 33
2.4 Expectation of a Random Variable 34
2.4.1 The Discrete Case 34
2.4.2 The Continuous Case 37
2.4.3 Expectation of a Function of a Random Variable 38
2.5 Jointly Distributed Random Variables 42
2.5.1 Joint Distribution Functions 42
2.5.2 Independent Random Variables 45
2.5.3 Covariance and Variance of Sums of Random Variables 46
2.5.4 Joint Probability Distribution of Functions of Random Variables 55
2.6 Moment Generating Functions 58
2.6.1 The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population 66
2.7 The Distribution of the Number of Events that Occur 69
2.8 Limit Theorems 71
2.9 Stochastic Processes 77
Exercises 79
References 91
3 Conditional Probability and Conditional Expectation 93
3.1 Introduction 93
3.2 The Discrete Case 93
3.3 The Continuous Case 97
3.4 Computing Expectations by Conditioning 100
3.4.1 Computing Variances by Conditioning 111
3.5 Computing Probabilities by Conditioning 115
3.6 Some Applications 133
3.6.1 A List Model 133
3.6.2 A Random Graph 135
3.6.3 Uniform Priors, Polya’s Urn Model, and Bose—Einstein Statistics 141
3.6.4 Mean Time for Patterns 146
3.6.5 The k-Record Values of Discrete Random Variables 149
3.6.6 Left Skip Free Random Walks 152
3.7 An Identity for Compound Random Variables 157
3.7.1 Poisson Compounding Distribution 160
3.7.2 Binomial Compounding Distribution 161
3.7.3 A Compounding Distribution Related to the Negative Binomial 162
Exercises 163
4 Markov Chains 183
4.1 Introduction 183
4.2 Chapman–Kolmogorov Equations 187
4.3 Classification of States 194
4.4 Long-Run Proportions and Limiting Probabilities 204
4.4.1 Limiting Probabilities 219
4.5 Some Applications 220
4.5.1 The Gambler’s Ruin Problem 220
4.5.2 A Model for Algorithmic Efficiency 223
4.5.3 Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem 226
4.6 Mean Time Spent in Transient States 231
4.7 Branching Processes 234
4.8 Time Reversible Markov Chains 237
4.9 Markov Chain Monte Carlo Methods 247
4.10 Markov Decision Processes 251
4.11 Hidden Markov Chains 254
4.11.1 Predicting the States 259
Exercises 261
References 275
5 The Exponential Distribution and the Poisson Process 277
5.1 Introduction 277
5.2 The Exponential Distribution 278
5.2.1 Definition 278
5.2.2 Properties of the Exponential Distribution 280
5.2.3 Further Properties of the Exponential Distribution 287
5.2.4 Convolutions of Exponential Random Variables 293
5.3 The Poisson Process 297
5.3.1 Counting Processes 297
5.3.2 Definition of the Poisson Process 298
5.3.3 Interarrival and Waiting Time Distributions 301
5.3.4 Further Properties of Poisson Processes 303
5.3.5 Conditional Distribution of the Arrival Times 309
5.3.6 Estimating Software Reliability 320
5.4 Generalizations of the Poisson Process 322
5.4.1 Nonhomogeneous Poisson Process 322
5.4.2 Compound Poisson Process 327
5.4.3 Conditional or Mixed Poisson Processes 332
5.5 Random Intensity Functions and Hawkes Processes 334
Exercises 338
References 356
6 Continuous-Time Markov Chains 357
6.1 Introduction 357
6.2 Continuous-Time Markov Chains 358
6.3 Birth and Death Processes 359
6.4 The Transition Probability Function Pij(t) 366
6.5 Limiting Probabilities 374
6.6 Time Reversibility 380
6.7 The Reversed Chai
