《華章數學原版精品系列:隨機模型概論(英文版·第4版)》的目標是介紹隨機建模的基本概念和方法，闡明隨機過程在科學領域中的各種套用，其主要內容包括條件機率與條件期望、馬爾可夫鏈、泊松過程、連續時間馬爾可夫鏈、布朗運動及相關過程、排隊系統、隨機發展和特徵函式及其套用等。此外，每節後都配有大量與實際問題相關的練習，便於讀者鞏固、提高。
基本介紹
- 書名：華章數學原版精品系列:隨機模型概論
- 作者：品斯基 (Mark Pinsky) 卡爾林 (Samuel Karlin)
- 出版社：機械工業出版社
- 頁數：563頁
- 開本：16
- 定價：69.00
- 外文名：An Introduction to Stochastic Modeling
- 類型：科學與自然
- 出版日期：2013年2月1日
- 語種：簡體中文, 英語
- ISBN：9787111412311
- 品牌：機械工業出版社
基本介紹,內容簡介,作者簡介,圖書目錄,名人推薦,
基本介紹
內容簡介
《華章數學原版精品系列:隨機模型概論(英文版·第4版)》適合作為一學期隨機過程課程的教材，需要讀者有初等機率論和微積分基礎。
作者簡介
作者：（美國）品斯基（Mark Pinsky） （美國）卡爾林（Samuel Karlin）
Mark A.Pinsky於1966年獲得麻省理工學院博士學位，之後在史丹福大學從事兩年博士後研究，現為西北大學數學系教授。他的主要研究方向是機率論、數學分析、傅立葉分析和小波。他發表論文120餘篇，出版圖書10本。
Samuel Karlin（1924——2007）著名數學家，他於1947年獲得普林斯頓大學數學專業博士學位，1948—1956年任教於加州理工學院。之後成為史丹福大學數學與統計學的教授。Karlin在數理經濟學、生物信息學、博弈論、進化論、生物分子序列分析等方面都做出了大量貢獻。
Mark A.Pinsky於1966年獲得麻省理工學院博士學位，之後在史丹福大學從事兩年博士後研究，現為西北大學數學系教授。他的主要研究方向是機率論、數學分析、傅立葉分析和小波。他發表論文120餘篇，出版圖書10本。
Samuel Karlin（1924——2007）著名數學家，他於1947年獲得普林斯頓大學數學專業博士學位，1948—1956年任教於加州理工學院。之後成為史丹福大學數學與統計學的教授。Karlin在數理經濟學、生物信息學、博弈論、進化論、生物分子序列分析等方面都做出了大量貢獻。
圖書目錄
Preface to the Fourth Edition
Preface to the Third Edition
Preface to the First Edition
To the Instructor
Acknowledgments
Introduction
1.1 Stochastic Modeling
1.1.1 Stochastic Processes
1.2 Probability Review
1.2.1 Events and Probabilities
1.2.2 Random Variables
1.2.3 Moments and Expected Values
1.2.4 Joint Distribution Functions
1.2.5 Sums and Convolutions
1.2.6 Change of Variable
1.2.7 Conditional Probability
1.2.8 Review of Axiomatic Probability Theory
1.3 The Major Discrete Distributions
1.3.1 Bernoulli Distribution
1.3.2 Binomial Distribution
1.3.3 Geometric and Negative Binominal Distributions
1.3.4 The Poisson Distribution
1.3.5 The Multinomial Distribution
1.4 Important Continuous Distributions
1.4.1 The Normal Distribution
1.4.2 The Exponential Distribution
1.4.3 The Uniform Distribution
1.4.4 The Gamma Distribution
1.4.5 The Beta Distribution
1.4.6 The Joint Normal Distribution
1.5 Some Elementary Exercises
1.5.1 Tail Probabilities
1.5.2 The Exponential Distribution
1.6 Useful Functions， Integrals， and Sums
Conditional Probability and Conditional Expectation
2.1 The Discrete Case
2.2 The Dice Game Craps
2.3 Random Sums
2.3.1 Conditional Distributions： The Mixed Case
2.3.2 The Moments of a Random Sum
2.3.3 The Distribution of a Random Sum
2.4 Conditioning on a Continuous Random Variable
2.5 Martingales
2.5.1 The Definition
2.5.2 The Markov Inequality
2.5.3 The Maximal Inequality for Nonnegative Martingales
Markov Chains： Introduction
3.1 Definitions
3.2 Transition Probability Matrices of a Markov Chain
3.3 Some Markov Chain Models
3.3.1 An Inventory Model
3.3.2 The Ehrenfest Um Model
3.3.3 Markov Chains in Genetics
3.3.4 A Discrete Queueing Markov Chain
3.4 First Step Analysis
3.4.1 Simple First Step Analyses
3.4.2 The General Absorbing Markov Chain
3.5 Some Special Markov Chains
3.5.1 The Two—State Markov Chain
3.5.2 Markov Chains Defined by Independent
Random Variables
3.5.3 One—Dimensional Random Walks
3.5.4 Success Runs
3.6 Functionals of Random Walks and Success Runs
3.6.1 The General Random Walk
3.6.2 Cash Management
3.6.3 The Success Runs Markov Chain
3.7 Another Look at First Step Analysis
3.8 Branching Processes
3.8.1 Examples of Branching Processes
3.8.2 The Mean and Variance of a Branching Process
3.8.3 Extinction Probabilities
3.9 Branching Processes and Generating Functions
3.9.1 Generating Functions and Extinction Probabilities
3.9.2 Probability Generating Functions and Sums of
Independent Random Variables
3.9.3 Multiple Branching Processes
4 The Long Run Behavior of Markov Chains
4.1 Regular Transition Probability Matrices
4.1.1 Doubly Stochastic Matrices
4.1.2 Interpretation of the Limiting Distribution
4.2 Examples
4.2.1 Including History in the State Description
4.2.2 Reliability and Redundancy
4.2.3 A Continuous Sampling Plan
4.2.4 Age Replacement Policies
4.2.5 Optimal Replacement Rules
4.3 The Classification of States
4.3.1 Irreducible Markov Chains
4.3.2 Periodicity of a Markov Chain
4.3.3 Recurrent and Transient States
4.4 The Basic Limit Theorem of Markov Chains
4.5 Reducible Markov Chains
Poisson Processes
5.1 The Poisson Distribution and the Poisson Process
5.1.1 The Poisson Distribution
5.1.2 The Poisson Process
5.1.3 Nonhomogeneous Processes
5.1.4 Cox Processes
5.2 The Law of Rare Events
5.2.1 The Law of Rare Events and the Poisson Process
5.2.2 Proof of Theorem 5.3
5.3 Distributions Associated with the Poisson Process
5.4 The Uniform Distribution and Poisson Processes
5.4.1 Shot Noise
5.4.2 Sum Quota Sampling
5.5 Spatial Poisson Processes
5.6 Compound and Marked Poisson Processes
5.6.1 Compound Poisson Processes
5.6.2 Marked Poisson Processes
Continuous Time Markov Chains
6.1 Pure Birth Processes
6.1.1 Postulates for the Poisson Process
6.1.2 Pure Birth Process
6.1.3 The Yule Process
6.2 Pure Death Processes
6.2.1 The Linear Death Process
6.2.2 Cable Failure Under Static Fatigue
6.3 Birth and Death Processes
6.3.1 Postulates
6.3.2 Sojourn Times
6.3.3 Differential Equations of Birth and Death Processes
6.4 The Limiting Behavior of Birth and Death Processes
6.5 Birth and Death Processes with Absorbing States
6.5.1 Probability of Absorption into State
6.5.2 Mean Time Until Absorption
6.6 Finite—State Continuous Time Markov Chains
6.7 A Poisson Process with a Markov Intensity
Renewal Phenomena
7.1 Definition of a Renewal Process and Related Concepts
7.2 Some Examples of Renewal Processes
7.2.1 Brief Sketches of Renewal Situations
7.2.2 Block Replacement
7.3 The Poisson Process Viewed as a Renewal Process
7.4 The Asymptotic Behavior of Renewal Processes
7.4. l The Elementary Renewal Theorem
7.4.2 The Renewal Theorem for Continuous Lifetimes
7.4.3 The Asymptotic Distribution of N（t）
7.4.4 The Limiting Distribution of Age and Excess Life
7.5 Generalizations and Variations on Renewal Processes
7.5.1 Delayed Renewal Processes
7.5.2 Stationary Renewal Processes
7.5.3 Cumulative and Related Processes
7.6 Discrete Renewal Theory
7.6.1 The Discrete Renewal Theorem
7.6.2 Deterministic Population Growth with Age Distribution
Brownian Motion and Related Processes
Queueing Systems
10 Random Evolutions
11 Characteristic Functions and Their Applications
Further Reading
Answers to Exercises
Index
Preface to the Third Edition
Preface to the First Edition
To the Instructor
Acknowledgments
Introduction
1.1 Stochastic Modeling
1.1.1 Stochastic Processes
1.2 Probability Review
1.2.1 Events and Probabilities
1.2.2 Random Variables
1.2.3 Moments and Expected Values
1.2.4 Joint Distribution Functions
1.2.5 Sums and Convolutions
1.2.6 Change of Variable
1.2.7 Conditional Probability
1.2.8 Review of Axiomatic Probability Theory
1.3 The Major Discrete Distributions
1.3.1 Bernoulli Distribution
1.3.2 Binomial Distribution
1.3.3 Geometric and Negative Binominal Distributions
1.3.4 The Poisson Distribution
1.3.5 The Multinomial Distribution
1.4 Important Continuous Distributions
1.4.1 The Normal Distribution
1.4.2 The Exponential Distribution
1.4.3 The Uniform Distribution
1.4.4 The Gamma Distribution
1.4.5 The Beta Distribution
1.4.6 The Joint Normal Distribution
1.5 Some Elementary Exercises
1.5.1 Tail Probabilities
1.5.2 The Exponential Distribution
1.6 Useful Functions， Integrals， and Sums
Conditional Probability and Conditional Expectation
2.1 The Discrete Case
2.2 The Dice Game Craps
2.3 Random Sums
2.3.1 Conditional Distributions： The Mixed Case
2.3.2 The Moments of a Random Sum
2.3.3 The Distribution of a Random Sum
2.4 Conditioning on a Continuous Random Variable
2.5 Martingales
2.5.1 The Definition
2.5.2 The Markov Inequality
2.5.3 The Maximal Inequality for Nonnegative Martingales
Markov Chains： Introduction
3.1 Definitions
3.2 Transition Probability Matrices of a Markov Chain
3.3 Some Markov Chain Models
3.3.1 An Inventory Model
3.3.2 The Ehrenfest Um Model
3.3.3 Markov Chains in Genetics
3.3.4 A Discrete Queueing Markov Chain
3.4 First Step Analysis
3.4.1 Simple First Step Analyses
3.4.2 The General Absorbing Markov Chain
3.5 Some Special Markov Chains
3.5.1 The Two—State Markov Chain
3.5.2 Markov Chains Defined by Independent
Random Variables
3.5.3 One—Dimensional Random Walks
3.5.4 Success Runs
3.6 Functionals of Random Walks and Success Runs
3.6.1 The General Random Walk
3.6.2 Cash Management
3.6.3 The Success Runs Markov Chain
3.7 Another Look at First Step Analysis
3.8 Branching Processes
3.8.1 Examples of Branching Processes
3.8.2 The Mean and Variance of a Branching Process
3.8.3 Extinction Probabilities
3.9 Branching Processes and Generating Functions
3.9.1 Generating Functions and Extinction Probabilities
3.9.2 Probability Generating Functions and Sums of
Independent Random Variables
3.9.3 Multiple Branching Processes
4 The Long Run Behavior of Markov Chains
4.1 Regular Transition Probability Matrices
4.1.1 Doubly Stochastic Matrices
4.1.2 Interpretation of the Limiting Distribution
4.2 Examples
4.2.1 Including History in the State Description
4.2.2 Reliability and Redundancy
4.2.3 A Continuous Sampling Plan
4.2.4 Age Replacement Policies
4.2.5 Optimal Replacement Rules
4.3 The Classification of States
4.3.1 Irreducible Markov Chains
4.3.2 Periodicity of a Markov Chain
4.3.3 Recurrent and Transient States
4.4 The Basic Limit Theorem of Markov Chains
4.5 Reducible Markov Chains
Poisson Processes
5.1 The Poisson Distribution and the Poisson Process
5.1.1 The Poisson Distribution
5.1.2 The Poisson Process
5.1.3 Nonhomogeneous Processes
5.1.4 Cox Processes
5.2 The Law of Rare Events
5.2.1 The Law of Rare Events and the Poisson Process
5.2.2 Proof of Theorem 5.3
5.3 Distributions Associated with the Poisson Process
5.4 The Uniform Distribution and Poisson Processes
5.4.1 Shot Noise
5.4.2 Sum Quota Sampling
5.5 Spatial Poisson Processes
5.6 Compound and Marked Poisson Processes
5.6.1 Compound Poisson Processes
5.6.2 Marked Poisson Processes
Continuous Time Markov Chains
6.1 Pure Birth Processes
6.1.1 Postulates for the Poisson Process
6.1.2 Pure Birth Process
6.1.3 The Yule Process
6.2 Pure Death Processes
6.2.1 The Linear Death Process
6.2.2 Cable Failure Under Static Fatigue
6.3 Birth and Death Processes
6.3.1 Postulates
6.3.2 Sojourn Times
6.3.3 Differential Equations of Birth and Death Processes
6.4 The Limiting Behavior of Birth and Death Processes
6.5 Birth and Death Processes with Absorbing States
6.5.1 Probability of Absorption into State
6.5.2 Mean Time Until Absorption
6.6 Finite—State Continuous Time Markov Chains
6.7 A Poisson Process with a Markov Intensity
Renewal Phenomena
7.1 Definition of a Renewal Process and Related Concepts
7.2 Some Examples of Renewal Processes
7.2.1 Brief Sketches of Renewal Situations
7.2.2 Block Replacement
7.3 The Poisson Process Viewed as a Renewal Process
7.4 The Asymptotic Behavior of Renewal Processes
7.4. l The Elementary Renewal Theorem
7.4.2 The Renewal Theorem for Continuous Lifetimes
7.4.3 The Asymptotic Distribution of N（t）
7.4.4 The Limiting Distribution of Age and Excess Life
7.5 Generalizations and Variations on Renewal Processes
7.5.1 Delayed Renewal Processes
7.5.2 Stationary Renewal Processes
7.5.3 Cumulative and Related Processes
7.6 Discrete Renewal Theory
7.6.1 The Discrete Renewal Theorem
7.6.2 Deterministic Population Growth with Age Distribution
Brownian Motion and Related Processes
Queueing Systems
10 Random Evolutions
11 Characteristic Functions and Their Applications
Further Reading
Answers to Exercises
Index
名人推薦
“這是一本非常好的教材……表述清晰、嚴謹，內容詳盡，循序漸進地引導讀者深入了解隨機模型。在我看來，本書最主要的優點是在介紹一些理論後給出恰當的套用，並且在每節都配有大量練習。”
——Martin crowder，薩里大學
——Martin crowder，薩里大學
