随机过程探究

图书标准信息

• 作者 雷斯尼克 编
• 出版社 世界图书出版公司
• 出版时间 2011-01
• 版次 1
• ISBN 9787510029721
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 626页
• 正文语种 英语

【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
CHAPTER1.PRELIMINARIES"DISCRETEINDEXSETSAND/ORDISCRETESTATESPACES
1.1.Non-negativeintegervaluedrandomvariables
1.2.Convolution
1.3.Generatingfunctions
1.3.1.Differentiationofgeneratingfunctions
1.3.2.Generatingfunctionsandmoments
1.3.3.Generatingfunctionsandconvolution
1.3.4.Generatingfunctions，compoundingandrandomsums
1.4.Thesimplebranchingprocess
1.5.Limitdistributionsandthecontinuitytheorem
1.5.1.Thelawofrareevents
1.6.Thesimplerandomwalk
1.7.Thedistributionofaprocess*
1.8.Stoppingtimes*
1.8.1.Wald'sidentity
1.8.2.Splittinganiidsequenceatastoppingtime
ExercisesforChapter1

CHAPTER2.MARKOVCHAINS
2.1.Constructionandfirstproperties
2.2.Examples
2.3.Higherordertransitionprobabilities
2.4.Decompositionofthestatespace
2.5.Thedissectionprinciple
2.6.Transienceandrecurrence
2.7.Periodicity
2.8.Solidarityproperties
2.9.Examples
2.10.Canonicaldecomposition
2.11.Absorptionprobabilities
2.12.Invariantmeasuresandstationarydistributions
2.12.1.Timeaverages
2.13.Limitdistributions
2.13.1Moreonnullrecurrenceandtransience*
2.14.Computationofthestationarydistribution
2.15.Classificationtechniques
ExercisesforChapter2

CHAPTER3.RENEWALTHEORY
3.1.Basics
3.2.Analyticinterlude
3.2.1.Integration
3.2.2.Convolution
3.2.3.Laplacetransforms
3.3.Countingrenewals
3.4.Renewalrewardprocesses
3.5.Therenewalequation
3.5.1.Riskprocesses*
3.6.ThePoissonprocessasarenewalprocess
3.7.Informaldiscussionofrenewallimittheorems;regenerativeprocesses
3.7.1Aninformaldiscussionofregenerativeprocesses
3.8.Discreterenewaltheory
3，9.Stationaryrenewalprocesses*.
3.10.Blackwellandkeyrenewaltheorems*.
3.10.1.DirectRiemannintegrability*
3.10.2.Equivalentformsoftherenewaltheorems*
3.10.3.Proofoftherenewaltheorem*
3.11.Improperrenewalequations
3.12.Moreregenerativeprocesses*
3.12.1.Definitionsandexamples*
3.12.2.TherenewalequationandSmith'stheorem*
3.12.3.Queueingexamples
ExercisesforChapter3

CHAPTER4.POINTPROCESSES
4.1.Basics
4.2.ThePoissonprocess
4.3.TransformingPoissonprocesses
4.3.1.Max-stableandstablerandomvariables*
4.4.Moretransformationtheory;markingandthinning
4.5.Theorderstatisticproperty
4.6.VariantsofthePoissonprocess
4.7.Technicalbasics*
4.7.1.TheLaplacefunctional*
4.8.MoreonthePoissonprocess*
4.9.AgeneralconstructionofthePoissonprocess;asimplederivationoftheorderstatisticproperty*
4.10.Moretransformationtheory;locationdependentthinning*
4.11.Records*
ExercisesforChapter4

CHAPTER5.CONTINUOUSTIMEMARKOVCHAINS
5.1.Defiuitionsandconstruction
5.2.Stabilityandexplosions
5.2.1.TheMarkovproperty*.
5.3.Dissection
5.3.1.Moredetailondissection*
5.4.Thebackwardequationandthegeneratormatrix
5.5.Stationaryandlimitingdistributions
5.5.1.Moreoninvariantmeasures*
5.6.Laplacetransformmethods
5.7.Calculationsandexamples
5.7.1.Queueingnetworks
5.8.Timedependentsolutions*
5.9.Reversibility
5.10.Uniformizability
5.11.Thelinearbirthprocessasapointprocess
ExercisesforChapter5

CHAPTER6.BROWNIANMOTION
6.1.Introduction
6.2.Preliminaries
6.3.ConstructionofBrownianmotion*
6.4.SimplepropertiesofstandardBrownianmotion
6.5.Thereflectionprincipleandthedistributionofthemaximum
6.6.Thestrongindependentincrementpropertyandreflection*
6.7.Escapefromastrip
6.8.Brownianmotionwithdrift
6.9.Heavytrafficapproximationsinqueueingtheory
6.10.TheBrownianbridgeandtheKolmogorov--Smirnovstatistic.
6.11.Pathproperties*
6.12.Quadraticvariation
6.13.Khintchine'slawoftheiteratedlogarithmforBrownianmotion
ExercisesforChapter6

CHAPTER7.THEGENERALRANDOMWALK*
7.1.Stoppingtimes
7.2.Globalproperties
7.3.PreludetoWiener-Hopf：Probabilisticinterpretationsoftransforms
7.4.Dualpairsofstoppingtimes
7.5.Wiener-Hopfdecompositions
7.6.ConsequencesoftheWiener-Hopffactorization
7.7.Themaximumofarandomwalk
7.8.RandomwalksandtheG/G/1queue
7.8.1.Exponentialrighttail
7.8.2.ApplicationtoG/M/1queueingmodel
7.8.3.Exponentiallefttail
7.8.4.TheM/G/1queue
7.8.5.Queuelengths
References
Index