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[美]丹尼尔斯特鲁克(Strook D.W) 著 / 世界图书出版公司 / 2009-04 / 平装
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Tosomeextent,itwouldbeaccuratetosummarizethecontentsofthisbookasanintolerablyprotracteddescriptionofwhathappenswheneitheroneraisesatransitionprobabilitymatrixP(i.e.,allentries(P)oarenonnegativeandeachrowofPsumsto1)tohigherandhigherpowersoroneexponentiatesR(P-I),whereRisadiagonalmatrixwithnon-negativeentries.Indeed,whenitcomesrightdowntoit,thatisallthatisdoneinthisbook.However,I,andothersofmyilk,wouldtakeoffenseatsuchadismissivecharacterizationofthetheoryofMarkovchainsandprocesseswithvaluesinacountablestatespace,andaprimarygoalofmineinwritingthisbookwastoconvinceitsreadersthatouroffensewouldbewarranted
Preface.Chapter1RandomWalksAGoodPlacetoBegin1.1.NearestNeighborRandomWlalksonZ1.1.1.DistributionatTimen1.1.2.PassageTimesviatheReflectionPrinciple1.1.3.SomeRelatedComputations1.1.4.TimeofFirstReturn1.1.5.PassageTimesviaFunctionalEquations1.2.RecurrencePropertiesofRandomWalks1.2.1.RandomWalksonZd1.2.2.AnElementaryRecurrenceCriterion1.2.3.RecurrenceofSymmetricRandomWalkinZ21.2.4.nansienceinZ31.3.ExercisesChapter2DoeblinSTheoryforMarkovChains2.1.SomeGeneralities2.1.1.ExistenceofMarkovChains2.1.2.TransionProbabilities&ProbabilityVectors2.1.3.nansitionProbabilitiesandFunctions2.1.4.TheMarkovProperty2.2.DoeblinSTheory2.2.1.DoeblinSBasicTheorem2.2.2.ACoupleofExtensions2.3.ElementsofErgodicTheory2.3.1.TheMeanErgodicTheorem2.3.2.ReturnTimes2.3.3.Identificationofπ2.4.ExercisesChapter3MoreabouttheErgodicTheoryofMarkovChains3.1.ClassificationofStates3.1.1.Classification,Recurrence,andTransience3.1.2.CriteriaforRecurrenceandTransmnge3.1.3.Periodicity3.2.ErgodicTheorywithoutDoeblin3.2.1.ConvergenceofMatrices3.2.2.AbelConvergence3.2.3.StructureofStationaryDistributions3.2.4.ASmallImprovement3.2.5.TheMcanErgodicTheoremAgain3.2.6.ARefinementinTheAperiodicCase3.2.7.PeriodicStructure3.3.ExercisesChapter4MarkovProcessesinContinuousTime4.1.PoissonProcesses4.1.1.TheSimplePoissonProcess4.1.2.CompoundPoissonProcessesonZ4.2.MarkovProcesseswithBoundedRates4.2.1.BasicConstruction4.2.2.TheMarkovProperty4.2.3.TheQ-MatrixandKolmogorovSBackwardEquation4.2.4.KolmogorovSForwardEquation4.2.5.SolvingKolmogorovSEquation4.2.6.AMarkovProcessfromitsInfinitesimalCharacteristics..4.3.UnboundedRates4.3.1.Explosion4.3.2.CriteriaforNon.explosionorExplosion4.3.3.WhattoDoWhenExplosionOccurs4.4.ErgodicProperties4.4.1.ClassificationofStates4.4.2.StationaryMeasuresandLimitTheorems4.4.3.Interpretingπii4.5.ExercisesChapter5ReversibleMarkovProeesses5.1.R,eversibleMarkovChains5.1.1.ReversibilityfromInvariance5.1.2.MeasurementsinQuadraticMean5.1.3.TheSpectralGap5.1.4.ReversibilityandPeriodicity5.1.5.RelationtoConvergenceinVariation5.2.DirichletFormsandEstimationofβ5.2.1.TheDirichletFormandPoincar4SInequality5.2.2.Estimatingβ+5.2.3.Estimatingβ-5.3.ReversibleMarkovProcessesinContinuousTime5.3.1.CriterionforReversibility5.3.2.ConvergenceinL2(π)forBoundedRates5.3.3.L2(π)ConvergenceRateinGeneral5.3.4.Estimating5.4.GibbsStatesandGlauberDynamics5.4.1.Formulation5.4.2.TheDirichletForm5.5.SimulatedAnnealing5.5.1.TheAlgorithm5.5.2.ConstructionoftheTransitionProbabilities5.5.3.DescriptionoftheMarkovProcess5.5.4.ChoosingaCoolingSchedule5.5.5.SmallImprovements5.6.ExercisesChapter6SomeMildMeasureTheory6.1.ADescriptionofLebesguesMeasureTheory6.1.1.MeasureSpaces6.1.2.SomeConsequencesofCountableAdditivity6.1.3.Generatinga-Algebras6.1.4.MeasurableFunctions6.1.5.LebesgueIntegration6.1.6.StabilityPropertiesofLebesgueIntegration6.1.7.LebesgueIntegrationinCountableSpaces6.1.8.FubinisTheorem6.2.ModelingProbability6.2.1.ModelingInfinitelyManyTossesofaFairCoin6.3.IndependentRandomVariables6.3.1.ExistenceofLotsofIndependentRandomVariables6.4.ConditionalProbabilitiesandExpectations6.4.1.ConditioningwithRespecttoRandomVariablesNotationReferencesIndex
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