• 概率论和随机过程
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概率论和随机过程

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作者[美]凯罗勒夫(Leonid B.Koralov) 著

出版社世界图书出版公司

出版时间2012-06

版次2

装帧平装

货号A6

上书时间2024-12-23

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  • 作者 [美]凯罗勒夫(Leonid B.Koralov) 著
  • 出版社 世界图书出版公司
  • 出版时间 2012-06
  • 版次 2
  • ISBN 9787510044106
  • 定价 55.00元
  • 装帧 平装
  • 开本 24开
  • 纸张 胶版纸
  • 页数 353页
  • 正文语种 英语
  • 原版书名 Theory of Probability and Random Processes (2nd ed.)(Universitext)
【内容简介】
Thisbookisprimarilybasedonaone-yearcoursethathasbeentaughtforanumberofyearsatPrincetonUniversitytoadvancedundergraduateandgraduatestudents.DuringthelastyearasimilarcoursehasalsobeentaughtattheUniversityofMaryland.
WewouldliketoexpressourthankstoMs.SophieLucasandProf.RafaelHerrerawhoreadthemanuscriptandsuggestedmanycorrections.WeareparticularlygratefultoProf.BorisGurevichformakingmanyimportantsug-gestionsonboththemathematicalcontentandstyle.
Whilewritingthisbook,L.KoralovwassupportedbyaNationalSci-enceFoundationgrant(DMS-0405152).Y.SinaiwassupportedbyaNationalScienceFoundationgrant(DMS-0600996).
【目录】
PartⅠProbabilityTheory
1RandomVariablesandTheirDistributions
1.1SpacesofElementaryOutcomes,a-Algebras,andMeasures
1.2ExpectationandVarianceofRandomVariablesonaDiscreteProbabilitySpace
1.3ProbabilityofaUnionofEvents
1.4EquivalentFormulationsofa-Additivity,Borela-AlgebrasandMeasurability
1.5DistributionFunctionsandDensities
1.6Problems
2SequencesofIndependentTrials
2.1LawofLargeNumbersandApplications
2.2deMoivre-LaplaceLimitTheoremandApplications
2.3PoissonLimitTheorem.
2.4Problems
3LebesgueIntegralandMathematicalExpectation
3.1DefinitionoftheLebesgueIntegral
3.2InducedMeasuresandDistributionFunctions
3.3TypesofMeasuresandDistributionFunctions
3.4RemarksontheConstructionoftheLebesgueMeasure
3.5ConvergenceofFunctions,TheirIntegrals,andtheFubiniTheorem
3.6SignedMeasuresandtheR,adon-NikodymTheorem
3.7LpSpaces
3.8MonteCarloMethod
3.9Problems
4ConditionalProbabilitiesandIndependence
4.1ConditionalProbabilities
4.2IndependenceofEvents,Algebras,andRandomVariables
4.3
4.4Problems
5MarkovChainswithaFiniteNumberofStates
5.1StochasticMatrices
5.2MarkovChains
5.3ErgodicandNon-ErgodicMarkovChains
5.4LawofLargeNumbersandtheEntropyofaMarkovChain
5.5ProductsofPositiveMatrices
5.6GeneralMarkovChainsandtheDoeblinCondition
5.7Problems
6RandomWalksontheLatticeZd
6.1RecurrentandTransientR,andomWalks
6.2RandomWalkonZandtheRefiectionPrinciple
6.3ArcsineLaw
6.4Gambler'sRuinProblem
6.5Problems
7LawsofLarzeNumbers
7.1Definitions,theBorel-CantelliLemmas,andtheKolmogorovInequality
7.2KolmogorovTheoremsontheStrongLawofLargeNumbers
7.3Problems
8WeakConveraenceofMeasures
8.1DefnitionofWeakConvergence
8.2WeakConvergenceandDistributionFunctions
8.3WeakCompactness,Tightness,andtheProkhorovTheorem
8.4Problems
9CharacteristicFunctions
9.1DefinitionandBasicProperties
9.2CharacteristicFunctionsandWeakConvergence
9.3GaussianRandomVectors
9.4Problems
10LimitTheorems
10.1CentralLimitTheorem,theLindebergCondition
10.2LocalLimitTheorem
10.3CentralLimitTheoremandRenormalizationGrOUDTheorv
10.4ProbabilitiesofLargeDeviations
……
PartⅡRandomProcesses
Index
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