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内容简介

随机过程是建立各种类型的大量随机变量现象模型的必要依据，作为应用概率方向的一个工具，书中将离散空间，Markov链，更新理论，点过程，分支过程，随机游程，Brownian运动，这些论题都是生动地展现给读者。《随机过程探究》表述灵活，大量的例子，练习和应用，并有的计算机程序作支持，使得内容的立体感增强，易于理解，可以作为应用科学领域不同层次水平学生的对随机过程的入门教程。每章末附有大量的补充练习。

目录

Preface
CHAPTER 1.PRELIMINARIES" DISCRETE INDEX SETS AND/OR DISCRETE STATE SPACES
1.1.Non-negative integer valued random variables
1.2.Convolution
1.3.Generating functions
1.3.1.Differentiation of generating functions
1.3.2.Generating functions and moments
1.3.3.Generating functions and convolution
1.3.4.Generating functions， compounding and random sums
1.4.The simple branching process
1.5.Limit distributions and the continuity theorem
1.5.1.The law of rare events
1.6.The simple random walk
1.7.The distribution of a process*
1.8.Stopping times*
1.8.1.Wald's identity
1.8.2.Splitting an iid sequence at a stopping time
Exercises for Chapter 1

CHAPTER 2.MARKOV CHAINS
2.1.Construction and first properties
2.2.Examples
2.3.Higher order transition probabilities
2.4.Decomposition of the state space
2.5.The dissection principle
2.6.Transience and recurrence
2.7.Periodicity
2.8.Solidarity properties
2.9.Examples
2.10.Canonical decomposition
2.11.Absorption probabilities
2.12.Invariant measures and stationary distributions
2.12.1.Time averages
2.13.Limit distributions
2.13.1 More on null recurrence and transience*
2.14.Computation of the stationary distribution
2.15.Classification techniques
Exercises for Chapter 2

CHAPTER 3.RENEWAL THEORY
3.1.Basics
3.2.Analytic interlude
3.2.1.Integration
3.2.2.Convolution
3.2.3.Laplace transforms
3.3.Counting renewals
3.4.Renewal reward processes
3.5.The renewal equation
3.5.1.Risk processes*
3.6.The Poisson process as a renewal process
3.7.Informal discussion of renewal limit theorems; regenerative processes
3.7.1 An informal discussion of regenerative processes
3.8.Discrete renewal theory
3，9.Stationary renewal processes* .
3.10.Blackwell and key renewal theorems* .
3.10.1.Direct Riemann integrability*
3.10.2.Equivalent forms of the renewal theorems*
3.10.3.Proof of the renewal theorem*
3.11.Improper renewal equations
3.12.More regenerative processes*
3.12.1.Definitions and examples*
3.12.2.The renewal equation and Smith's theorem*
3.12.3.Queueing examples
Exercises for Chapter 3

CHAPTER 4.POINT PROCESSES
4.1.Basics
4.2.The Poisson process
4.3.Transforming Poisson processes
4.3.1.Max-stable and stable random variables*
4.4.More transformation theory; marking and thinning
4.5.The order statistic property
4.6.Variants of the Poisson process
4.7.Technical basics*
4.7.1.The Laplace functional*
4.8.More on the Poisson process*
4.9.A general construction of the Poisson process; a simple derivation of the order statistic property*
4.10.More transformation theory; location dependent thinning*
4.11.Records*
Exercises for Chapter 4

CHAPTER 5.CONTINUOUS TIME MARKOV CHAINS
5.1.Defiuitions and construction
5.2.Stability and explosions
5.2.1.The Markov property* .
5.3.Dissection
5.3.1.More detail on dissection*
5.4.The backward equation and the generator matrix
5.5.Stationary and limiting distributions
5.5.1.More on invariant measures*
5.6.Laplace transform methods
5.7.Calculations and examples
5.7.1.Queueing networks
5.8.Time dependent solutions*
5.9.Reversibility
5.10.Uniformizability
5.11.The linear birth process as a point process
Exercises for Chapter 5

CHAPTER 6.BROWNIAN MOTION
6.1.Introduction
6.2.Preliminaries
6.3.Construction of Brownian motion*
6.4.Simple properties of standard Brownian motion
6.5.The reflection principle and the distribution of the maximum
6.6.The strong independent increment property and reflection*
6.7.Escape from a strip
6.8.Brownian motion with drift
6.9.Heavy traffic approximations in queueing theory
6.10.The Brownian bridge and the Kolmogorov--Smirnov statistic.
6.11.Path properties*
6.12.Quadratic variation
6.13.Khintchine's law of the iterated logarithm for Brownian motion
Exercises for Chapter 6

CHAPTER 7.THE GENERAL RANDOM WALK*
7.1.Stopping times
7.2.Global properties
7.3.Prelude to Wiener-Hopf： Probabilistic interpretations of transforms
7.4.Dual pairs of stopping times
7.5.Wiener-Hopf decompositions
7.6.Consequences of the Wiener-Hopf factorization
7.7.The maximum of a random walk
7.8.Random walks and the G/G/1 queue
7.8.1.Exponential right tail
7.8.2.Application to G/M/1 queueing model
7.8.3.Exponential left tail
7.8.4.The M/G/1 queue
7.8.5.Queue lengths
References
Index

前言/序言

随机过程探究 [Adventures in Stochastic Processes] 电子书 下载 mobi epub pdf txt

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国学者在平稳过程、马尔科夫过程、鞅论、极限定理、随机微分方程等方面做出了较好的工作。

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研究随机过程的方法多种多样，主要可以分为两大类：一类是概率方法，其中用到轨道性质、停时和随机微分方程等；另一类是分析的方法，其中用到测度论、微分方程、半群理论、函数堆和希尔伯特空间等。实际研究中常常两种方法并用。另外组合方法和代数方法在某些特殊随机过程的研究中也有一定作用。研究的主要内容有：多指标随机过程、无穷质点与马尔可夫过程、概率

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随机过程(Stochastic Process)是一连串随机事件动态关系的定量描述。随机过程论与其他数学分支如位势论、微分方程、力学及复变函数论等有密切的联系，是在自然科学、工程科学及社会科学各领域研究随机现象的重要工具。随机过程论目前已得到广泛的应用，在诸如天气预报、统计物理、天体物理、运筹决策、经济数学、安全科学、人口理论、可靠性及计算机科学等很多领域都要经常用到随机过程的理论来建立数学模型。

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