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概率论

概率论
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作者: 编
出版社: 世界图书出版公司
2004-11
版次: 2
ISBN: 9787506271882
定价: 65.00
装帧: 平装
开本: 其他
纸张: 胶版纸
页数: 621页
分类: 自然科学
55人买过
  • InthePrefacetothefirstedition,originallypublishedin1980,wementionedthatthisbookwasbasedontheauthor'slecturesintheDepartmentofMechanicsandMathematicsoftheLomonosovUniversityinMoscow,whichwereissued,inpart,inmimeographedformunderthetitle"Probability,Statistics,andStochasticProcessors,I,II"andpublishedbythatUniversity.Ouroriginalintentioninwritingthefirsteditionofthisbookwastodividethecontentsintothreeparts：probability,mathematicalstatistics,andtheoryofstochasticprocesses,whichcorrespondstoanoutlineofathreesemestercourseoflecturesforuniversitystudentsofmathematics.However,inthecourseofpreparingthebook,itturnedouttobeimpossibletorealizethisintentioncompletely,sinceafullexpositionwouldhaverequiredtoomuchspace.Inthisconnection,westatedinthePrefacetothefirsteditionthatonlyprobabilitytheoryandthetheoryofrandomprocesseswithdiscretetimewerereallyadequatelypresented. 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
  • 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
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