[套装书]数学分析八讲(修订版)+应用随机过程:概率模型导论(英文版.第11版)

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内容简介: 《数学分析八讲(修订版)》
短短八讲,不仅让你了解数学分析的概貌,更让你领会数学分析的精髓。这本由著名苏联数学家和数学教育家辛钦潜心编著的经典教材,思路清晰,引人入胜,全面梳理了数学分析的主要内容,涉及连续统、极限、函数、级数、导数、积分、函数的级数展开以及微分方程等主题。
本书原是作者在国立莫斯科大学为工程师授课的教案。书中选材独到,叙述深入浅出,即使是只学过最简单的数学分析课程的人也能容易地阅读和理解。而以此为基 础,你可以更好地学习数学分析相关主题更为深入的内容。无论你是工程师、经济学者、数学教师,还是学习数学分析课程的大学生(包括非数学专业的大学生), 阅读本书都能获益匪浅。
本书根据苏联国立技术理论书籍出版社1948年第三版译出,本次修订改正了一些错误,新增加了一些注解。
《应用随机过程:概率模型导论(英文版.第11版)》
《应用随机过程 概率模型导论》是一部经典的随机过程著作, 叙述深入浅出、涉及面广。 主要内容有随机变量、条件期望、马尔可夫链、指数分布、泊松过程、平稳过程、更新理论及排队论等,也包括了随机过程在物理、生物、运筹、网络、遗传、经 济、保险、金融及可靠性中的应用。 特别是有关随机模拟的内容, 给随机系统运行的模拟计算提供了有力的工具。最新版还增加了不带左跳的随机徘徊和生灭排队模型等内容。本书约有700道习题, 其中带星号的习题还提供了解答。
《应用随机过程 概率模型导论》可作为概率论与数理统计、计算机科学、保险学、物理学、社会科学、生命科学、管理科学与工程学等专业随机过程基础课教材。

目录: 《数学分析八讲(修订版)》
第一讲 连续统
第二讲 极限
第三讲 函数
第四讲 级数
第五讲 导数
第六讲 积分
第七讲 函数的级数展开
第八讲 微分方程
译后记
《应用随机过程:概率模型导论(英文版.第11版)》
1 Introduction to Probability Theory
1.1 Introduction
1.2 Sample Space and Events
1.3 Probabilities Defined on Events
1.4 Conditional Probabilities
1.5 Independent Events
1.6 Bayes' Formula
Exercises
References
2 Random Variables
2.1 Random Variables
2.2 Discrete Random Variables
2.2.1 The Bernoulli Random Variable
2.2.2 The Binomial Random Variable
2.2.3 The Geometric Random Variable
2.2.4 The Poisson Random Variable
2.3 Continuous Random Variables
2.3.1 The Uniform Random Variable
2.3.2 Exponential Random Variables
2.3.3 Gamma Random Variables
2.3.4 Normal Random Variables
2.4 Expectation of a Random Variable
2.4.1 The Discrete Case
2.4.2 The Continuous Case
2.4.3 Expectation of a Function of a Random Variable
2.5 Jointly Distributed Random Variables
2.5.1 Joint Distribution Functions
2.5.2 Independent Random Variables
2.5.3 Covariance and Variance of Sums of Random Variables
2.5.4 Joint Probability Distribution of Functions of Random Variables
2.6 Moment Generating Functions
2.6.1 The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population
2.7 The Distribution of the Number of Events that Occur
2.8 Limit Theorems
2.9 Stochastic Processes
Exercises
References
3 Conditional Probability and Conditional Expectation
3.1 Introduction
3.2 The Discrete Case
3.3 The Continuous Case
3.4 Computing Expectations by Conditioning
3.4.1 Computing Variances by Conditioning
3.5 Computing Probabilities by Conditioning
3.6 Some Applications
3.6.1 A List Model
3.6.2 A Random Graph
3.6.3 Uniform Priors, Polya's Urn Model, and Bose-Einstein Statistics
3.6.4 Mean Time for Patterns
3.6.5 The k-Record Values of Discrete Random Variables
3.6.6 Left Skip Free Random Walks
3.7 An Identity for Compound Random Variables
3.7.1 Poisson Compounding Distribution
3.7.2 Binomial Compounding Distribution
3.7.3 A Compounding Distribution Related to the Negative Binomial
Exercises
4 Markov Chains
4.1 Introduction
4.2 Chapman-Kolmogorov Equations
4.3 Classification of States
4.4 Long-Run Proportions and Limiting Probabilities
4.4.1 Limiting Probabilities
4.5 Some Applications
4.5.1 The Gambler's Ruin Problem
4.5.2 A Model for Algorithmic Efficiency
4.5.3 Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem
4.6 Mean Time Spent in Transient States
4.7 Branching Processes
4.8 Time Reversible Markov Chains
4.9 Markov Chain Monte Carlo Methods
4.10 Markov Decision Processes
4.11 Hidden Markov Chains
4.11.1 Predicting the States
Exercises
References
5 The Exponential Distribution and the Poisson Process
5.1 Introduction
5.2 The Exponential Distribution
5.2.1 Definition
5.2.2 Properties of the Exponential Distribution
5.2.3 Further Properties of the Exponential Distribution
5.2.4 Convolutions of Exponential Random Variables
5.3 The Poisson Process
5.3.1 Counting Processes
5.3.2 Definition of the Poisson Process
5.3.3 Interarrival and Waiting Time Distributions
5.3.4 Further Properties of Poisson Processes
5.3.5 Conditional Distribution of the Arrival Times
5.3.6 Estimating Software Reliability
5.4 Generalizations of the Poisson Process
5.4.1 Nonhomogeneous Poisson Process
5.4.2 Compound Poisson Process
5.4.3 Conditional or Mixed Poisson Processes
5.5 Random Intensity Functions and Hawkes Processes
Exercises
References
6 Continuous-Time Markov Chains
6.1 Introduction
6.2 Continuous-Time Markov Chains
6.3 Birth and Death Processes
6.4 The Transition Probability Function Pij(t)
6.5 Limiting Probabilities
6.6 Time Reversibility
6.7 The Reversed Chain
……
7 Renewal Theory and Its Applications
8 Queueing Theory
9 Reliability Theory
10 Brownian Motion and Stationary Processes
11 Simulation
Appendix:Solutions to Starred Exercises
Index