概率论和随机过程

图书标准信息

• 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