概率论

图书标准信息

• 作者 A.N.Shiryaev 编
• 出版社 世界图书出版公司
• 出版时间 2004-11
• 版次 2
• ISBN 9787506271882
• 定价 65.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 621页

【内容简介】

InthePrefacetothefirstedition,originallypublishedin1980,wementionedthatthisbookwasbasedontheauthor'slecturesintheDepartmentofMechanicsandMathematicsoftheLomonosovUniversityinMoscow,whichwereissued,inpart,inmimeographedformunderthetitle"Probability,Statistics,andStochasticProcessors,I,II"andpublishedbythatUniversity.Ouroriginalintentioninwritingthefirsteditionofthisbookwastodividethecontentsintothreeparts：probability,mathematicalstatistics,andtheoryofstochasticprocesses,whichcorrespondstoanoutlineofathreesemestercourseoflecturesforuniversitystudentsofmathematics.However,inthecourseofpreparingthebook,itturnedouttobeimpossibletorealizethisintentioncompletely,sinceafullexpositionwouldhaverequiredtoomuchspace.Inthisconnection,westatedinthePrefacetothefirsteditionthatonlyprobabilitytheoryandthetheoryofrandomprocesseswithdiscretetimewerereallyadequatelypresented.

【目录】

PrefacetotheSecondEdition
PrefacetotheFirstEdition
Introduction
CHAPTERIElementaryProbabilityTheory
1.ProbabilisticModelofanExperimentwithaFiniteNumberofOutcomes
2.SomeClassicalModelsandDistributions
3.ConditionalProbability.Independence
4.RandomVariablesandTheirProperties
5.TheBernoulliScheme.I.TheLawofLargeNumbers
6.TheBernoulliScheme.II.LimitTheorems（Local，DeMoivre-Laplace，Poisson）
7.EstimatingtheProbabilityofSuccessintheBernoulliScheme
8.ConditionalProbabilitiesandMathematicalExpectationswithRespecttoDecompositions
9.RandomWalk.I.ProbabilitiesofRuinandMeanDurationinCoinTossing
10.RandomWalk.II.ReflectionPrinciple.ArcsineLaw
11.Martingales.SomeApplicationstotheRandomWalk
12.MarkovChains.ErgodicTheorem.StrongMarkovProperty

CHAPTERIIMathematicalFoundationsofProbabilityTheory
1.ProbabilisticModelforanExperimentwithInfinitelyManyOutcomes.Kolmogorov‘sAxioms
2.Algebrasanda-algebras.MeasurableSpaces
3.MethodsofIntroducingProbabilityMeasuresonMeasurableSpaces
……
CHAPTERIIIConergenceofProbabilityMeasures.CentralLimitTheorem
CHAPTERIVSequencesandSumsofIndependentRandomVariables
CHAPTERVStationary（StirctySense）RandomSequencesandErgodicTheory
CHAPTERVIStationary（WideSense）RandomSequencesL2Theory
CHAPTERVIISequencesofRandomVariablesthatFormMartingalse
CHAPTERVIIISequencesofRandomVariablesthatFormMarkovChains
HistoricalandBibographicalNotes
Refernces
IndexofSymbols
Index