隨機過程探究 [Adventures in Stochastic Processes] 下載 mobi epub pdf 電子書 2024

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隨機過程是建立各種類型的大量隨機變量現象模型的必要依據，作為應用概率方嚮的一個工具，書中將離散空間，Markov鏈，更新理論，點過程，分支過程，隨機遊程，Brownian運動，這些論題都是生動地展現給讀者。《隨機過程探究》錶述靈活，大量的例子，練習和應用，並有的計算機程序作支持，使得內容的立體感增強，易於理解，可以作為應用科學領域不同層次水平學生的對隨機過程的入門教程。每章末附有大量的補充練習。

目錄

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

隨機過程探究 [Adventures in Stochastic Processes] 下載 mobi epub pdf txt 電子書 格式

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高年級本科生和研究生用書，內容以及印刷都蠻好，京東送的也挺快。

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隨機過程

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理學的研究，如吉布斯、玻爾茲曼、龐加萊等人對統計力學的研究，及後來愛因斯坦、維納、萊維等人對布朗運動的開創性工作。1907年前後，馬爾可夫研究瞭一係列有特定相依性的隨機變量，後人稱之為馬爾可夫鏈。1923年維納給齣布朗運動的數學定義，直到今日這一過程仍是重要的研究課題。隨機過程一般理論的研究通常認為開始於20世紀30年代。1931年，柯爾莫哥洛夫發錶瞭《概率論的解析方法》，1934年A·辛欽發錶瞭《平穩過程的相關理論》，這兩篇著作奠定瞭馬爾可夫過程與平穩過程的理論基礎。1953年，杜布齣版瞭名著《隨機過程論》，係統且嚴格地敘述瞭隨機過程基本理論。

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