應用隨機過程概率模型導論

內(nèi)容概要

　　本書實例豐富，涉及多學科各種概率模型。主要內(nèi)容有隨機變量、條件概率及條件期望、離散及連續(xù)馬爾科夫鏈、指數(shù)分布、泊松過程、布朗運動及平穩(wěn)過程、更新理論及排隊論等，最后介紹了隨機模擬。本書寫得極其生動和直觀，并附有大量的不同領域的習題和實用的例子。　　本書可作為概率論與統(tǒng)計、計算機科學、保險學、物理學和社會科學、生命科學、管理科學與工程學專業(yè)隨機過程基礎課教材。

作者簡介

Sheldon M.Ross，國際知名統(tǒng)計學家，加州大學伯克利分校工業(yè)工程與運籌系教授。畢業(yè)于斯坦福大學統(tǒng)計系。研究領域包括：隨機模型、仿真模擬、統(tǒng)計分析、金融數(shù)學等。Ross教授是多本暢銷數(shù)學和統(tǒng)計教材的作者。

書籍目錄

1　Introduction to Probability Theory　11.1　Introduction　11.2　Sample Space and Events　11.3　Probabilities Defined on Events　41.4　Conditional Probabilities　71.5　Independent Events　101.6　Bayes' Formula　12Exercises　15References　212　Random Variables　232.1　Random Variables　232.2　Discrete Random Variables　272.3　Continuous Random Variables　342.4　Expectation of a Random Variable　382.5　Jointly Distributed Random Variables　432.6　Moment Generating Functions　642.7　Limit Theorems　772.8　Stochastic Processes　83Exercises　85References　963　Conditional Probability and Conditional Expectation　973.1　Introduction　973.2　The Discrete Case　973.3　The Continuous Case　1023.4　Computing Expectations by Conditioning　1053.5　Computing Probabilities by Conditioning　1193.6　Some Applications Exercises　136Exercises　1614　Markov Chains　1814.1　Introduction　1814.2　Chapman-Kolmogorov Equations　1854.3　Classification of States　1894.4　Limiting Probabilities　2004.5　Some Applications　2134.6　Mean Time Spent in Transient States　2264.7　Branching Processes　2284.8　Time Reversible Markov Chains　2324.9　Markov Chain Monte Carlo Methods　2434.10　Markov Decision Processes　248Exercises　252References　2685　The Exponential Distribution and the Poisson Process　2695.1　Introduction　2695.2　The Exponential Distribution　2705.3　The Poisson Process　2885.4　Generalizations of the Poisson Process　316Exercises　330References　3486　Continuous-Time Markov Chains　3496.1　Introduction　3496.2　Continuous-Time Markov Chains　3506.3　Birth and Death Processes　3526.4　The Transition Probability Function Pij (t)　3596.5　Limiting Probabilities　3686.6　Time Reversibility　3766.7　Uniformization　3846.8　Computing the Transition Probabilities　388Exercises　390References　3997　Renewal Theory and Its Applications　4017.1　Introduction　4017.2　Distribution of N(t)　4037.3　Limit Theorems and Their Applications　4077.4　Renewal Reward Processes　4167.5　Regenerative Processes　4257.6　Semi-Markov Processes　4347.7　The Inspection Paradox　4377.8　Computing the Renewal Function　4407.9　Applications to Patterns　4437.10　The Insurance Ruin Problem　455Exercises　460References　4728　Queueing Theory　4758.1　Introduction　4758.2　Preliminaries　4768.3　Exponential Models　4808.4　Network of Queues　4968.5　The System M/G/1　5078.6　Variations on the M/G/1　5108.7　The Model G/M/1　5198.8　A Finite Source Model　5258.9　Multiserver Queues　528Exercises　534References　5469　Reliability Theory　5479.1　Introduction　5479.2　Structure Functions　5479.3　Reliability of Systems of Independent Components　5549.4　Bounds on the Reliability Function　5599.5　System Life as a Function of Component Lives　5719.6　Expected System Lifetime　5809.7　Systems with Repair　586Exercises　593References　60010　Brownian Motion and Stationary Processes　60110.1　Brownian Motion　60110.2　Hitting Times, Maximum Variable, and the Gambler's Ruin Problem　60510.3　Variations on Brownian Motion　60710.4　Pricing Stock Options　60810.5　White Noise　62010.6　Gaussian Processes　62210.7　Stationary andWeakly Stationary Processes　62510.8　Harmonic Analysis of Weakly Stationary Processes　630Exercises　633References　63811　Simulation　63911.1　Introduction　63911.2　General Techniques for Simulating Continuous Random Variables　64411.3　Special Techniques for Simulating Continuous Random Variables　65311.4　Simulating from Discrete Distributions　66111.5　Stochastic Processes　66811.6　Variance Reduction Techniques　67911.7　Determining the Number of Runs　69611.8　Coupling from the Past　696Exercises　699References　707Appendix: Solutions to Starred Exercises　709Index　749

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