马尔科夫过程导论

图书标准信息

• 作者 [美]丹尼尔斯特鲁克（Strook D.W） 著
• 出版社 世界图书出版公司
• 出版时间 2009-04
• 版次 1
• ISBN 9787510004483
• 定价 25.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 171页
• 正文语种 英语

【内容简介】

　　Tosomeextent，itwouldbeaccuratetosummarizethecontentsofthisbookasanintolerablyprotracteddescriptionofwhathappenswheneitheroneraisesatransitionprobabilitymatrixP(i.e.，allentries(P)oarenonnegativeandeachrowofPsumsto1)tohigherandhigherpowersoroneexponentiatesR(P-I)，whereRisadiagonalmatrixwithnon-negativeentries.Indeed，whenitcomesrightdowntoit，thatisallthatisdoneinthisbook.However，I，andothersofmyilk，wouldtakeoffenseatsuchadismissivecharacterizationofthetheoryofMarkovchainsandprocesseswithvaluesinacountablestatespace，andaprimarygoalofmineinwritingthisbookwastoconvinceitsreadersthatouroffensewouldbewarranted

【目录】

Preface.
Chapter1RandomWalksAGoodPlacetoBegin
1.1.NearestNeighborRandomWlalksonZ
1.1.1.DistributionatTimen
1.1.2.PassageTimesviatheReflectionPrinciple
1.1.3.SomeRelatedComputations
1.1.4.TimeofFirstReturn
1.1.5.PassageTimesviaFunctionalEquations
1.2.RecurrencePropertiesofRandomWalks
1.2.1.RandomWalksonZd
1.2.2.AnElementaryRecurrenceCriterion
1.2.3.RecurrenceofSymmetricRandomWalkinZ2
1.2.4.nansienceinZ3
1.3.Exercises

Chapter2DoeblinSTheoryforMarkovChains
2.1.SomeGeneralities
2.1.1.ExistenceofMarkovChains
2.1.2.TransionProbabilities&ProbabilityVectors
2.1.3.nansitionProbabilitiesandFunctions
2.1.4.TheMarkovProperty
2.2.DoeblinSTheory
2.2.1.DoeblinSBasicTheorem
2.2.2.ACoupleofExtensions
2.3.ElementsofErgodicTheory
2.3.1.TheMeanErgodicTheorem
2.3.2.ReturnTimes
2.3.3.Identificationofπ
2.4.Exercises

Chapter3MoreabouttheErgodicTheoryofMarkovChains
3.1.ClassificationofStates
3.1.1.Classification，Recurrence，andTransience
3.1.2.CriteriaforRecurrenceandTransmnge
3.1.3.Periodicity
3.2.ErgodicTheorywithoutDoeblin
3.2.1.ConvergenceofMatrices
3.2.2.AbelConvergence
3.2.3.StructureofStationaryDistributions
3.2.4.ASmallImprovement
3.2.5.TheMcanErgodicTheoremAgain
3.2.6.ARefinementinTheAperiodicCase
3.2.7.PeriodicStructure
3.3.Exercises

Chapter4MarkovProcessesinContinuousTime
4.1.PoissonProcesses
4.1.1.TheSimplePoissonProcess
4.1.2.CompoundPoissonProcessesonZ
4.2.MarkovProcesseswithBoundedRates
4.2.1.BasicConstruction
4.2.2.TheMarkovProperty
4.2.3.TheQ-MatrixandKolmogorovSBackwardEquation
4.2.4.KolmogorovSForwardEquation
4.2.5.SolvingKolmogorovSEquation
4.2.6.AMarkovProcessfromitsInfinitesimalCharacteristics..
4.3.UnboundedRates
4.3.1.Explosion
4.3.2.CriteriaforNon.explosionorExplosion
4.3.3.WhattoDoWhenExplosionOccurs
4.4.ErgodicProperties
4.4.1.ClassificationofStates
4.4.2.StationaryMeasuresandLimitTheorems
4.4.3.Interpretingπii
4.5.Exercises

Chapter5ReversibleMarkovProeesses
5.1.R，eversibleMarkovChains
5.1.1.ReversibilityfromInvariance
5.1.2.MeasurementsinQuadraticMean
5.1.3.TheSpectralGap
5.1.4.ReversibilityandPeriodicity
5.1.5.RelationtoConvergenceinVariation
5.2.DirichletFormsandEstimationofβ
5.2.1.TheDirichletFormandPoincar4SInequality
5.2.2.Estimatingβ+
5.2.3.Estimatingβ-
5.3.ReversibleMarkovProcessesinContinuousTime
5.3.1.CriterionforReversibility
5.3.2.ConvergenceinL2(π)forBoundedRates
5.3.3.L2(π)ConvergenceRateinGeneral
5.3.4.Estimating
5.4.GibbsStatesandGlauberDynamics
5.4.1.Formulation
5.4.2.TheDirichletForm
5.5.SimulatedAnnealing
5.5.1.TheAlgorithm
5.5.2.ConstructionoftheTransitionProbabilities
5.5.3.DescriptionoftheMarkovProcess
5.5.4.ChoosingaCoolingSchedule
5.5.5.SmallImprovements
5.6.Exercises

Chapter6SomeMildMeasureTheory
6.1.ADescriptionofLebesguesMeasureTheory
6.1.1.MeasureSpaces
6.1.2.SomeConsequencesofCountableAdditivity
6.1.3.Generatinga-Algebras
6.1.4.MeasurableFunctions
6.1.5.LebesgueIntegration
6.1.6.StabilityPropertiesofLebesgueIntegration
6.1.7.LebesgueIntegrationinCountableSpaces
6.1.8.FubinisTheorem
6.2.ModelingProbability
6.2.1.ModelingInfinitelyManyTossesofaFairCoin
6.3.IndependentRandomVariables
6.3.1.ExistenceofLotsofIndependentRandomVariables
6.4.ConditionalProbabilitiesandExpectations
6.4.1.ConditioningwithRespecttoRandomVariables
Notation
References
Index