馬爾科夫過程導(dǎo)論

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作　者：	（美）丹尼爾斯特魯克（Strook,D.W）著
出版社：	世界圖書出版公司
叢編項(xiàng)：
標(biāo)　簽：	概率論與數(shù)理統(tǒng)計(jì)

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ISBN：	9787510004483	出版時(shí)間：	2009-04-01	包裝：	平裝
開本：	24開	頁(yè)數(shù)：	171	字?jǐn)?shù)：

內(nèi)容簡(jiǎn)介

　　To some extent， it would be accurate to summarize the contents of this book as an intolerably protracted description of what happens when either one raises a transition probability matrix P （i.e.， all entries （P）o are nonnegative and each row of P sums to 1） to higher and higher powers or one exponentiates R（P - I）， where R is a diagonal matrix with non-negative entries. Indeed， when it comes right down to it， that is all that is done in this book. However， I， and others of my ilk， would take offense at such a dismissive characterization of the theory of Markov chains and processes with values in a countable state space， and a primary goal of mine in writing this book was to convince its readers that our offense would be warranted

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圖書目錄

Preface.
Chapter1 RandomWalksAGoodPlacetoBegin
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
Chapter2 DoeblinSTheoryforMarkovChains
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
Chapter3 MoreabouttheErgodicTheoryofMarkovChains
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
Chapter4 MarkovProcessesinContinuousTime
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
Chapter5 ReversibleMarkovProeesses
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
Chapter6 SomeMildMeasureTheory
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