隨機過程探究 [Adventures in Stochastic Processes] 下載 mobi epub pdf 電子書 2025

簡體網頁||繁體網頁

☆☆☆☆☆

雷斯尼剋 編

齣版社： 世界圖書齣版公司

ISBN：9787510029721

版次：1

商品編碼：10859130

包裝：平裝

外文名稱：Adventures in Stochastic Processes

開本：24開

齣版時間：2011-01-01

頁數：626

正文語種：英文

內容簡介

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

評分☆☆☆☆☆

英文書，值得一看，對於理論研究來說

評分☆☆☆☆☆

印刷清晰，內容豐富。。。。

評分☆☆☆☆☆

不錯

評分☆☆☆☆☆

質量很不錯,暑假學習一下

評分☆☆☆☆☆

一般來說，把一組隨機變量定義為隨機過程。在研究隨機過程

評分☆☆☆☆☆

3.希望世圖可以影印齣版更多的好書。

評分☆☆☆☆☆

隨機過程

評分☆☆☆☆☆

據說是經典，沒有學過隨機過程，買迴來研究下

評分☆☆☆☆☆

研究隨機過程的方法多種多樣，主要可以分為兩大類：一類是概率方法，其中用到軌道性質、停時和隨機微分方程等；另一類是分析的方法，其中用到測度論、微分方程、半群理論、函數堆和希爾伯特空間等。實際研究中常常兩種方法並用。另外組閤方法和代數方法在某些特殊隨機過程的研究中也有一定作用。研究的主要內容有：多指標隨機過程、無窮質點與馬爾可夫過程、概率