马尔科夫过程导论

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		马尔科夫过程导论
		马尔科夫过程导论

基本信息·出版社：世界图书出版公司
·页码：171 页
·出版日期：2009年04月
·ISBN：7510004489/9787510004483
·条形码：9787510004483
·版本：第1版
·装帧：平装
·开本：24
·正文语种：英语
·外文书名：An Introduction to Markov Processes

内容简介 《马尔科夫过程导论》讲述了：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
编辑推荐 《马尔科夫过程导论》是由世界图书出版公司出版的。
目录
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 Doeblin'STheoryforMarkovChains
2.1.SomeGeneralities
2.1.1.ExistenceofMarkovChains
2.1.2.TransionProbabilities&ProbabilityVectors
2.1.3.nansitionProbabilitiesandFunctions
2.1.4.TheMarkovProperty
2.2.Doeblin'STheory
2.2.1.Doeblin'SBasicTheorem
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-MatrixandKolmogorov'SBackwardEquation
4.2.4.Kolmogorov'SForwardEquation
4.2.5.SolvingKolmogorov'SEquation
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.TheDirichletFormandPoincar4'SInequality
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.ADescriptionofLebesgue'sMeasureTheory
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.Fubini'sTheorem
6.2.ModelingProbability
6.2.1.ModelingInfinitelyManyTossesofaFairCoin
6.3.IndependentRandomVariables
6.3.1.ExistenceofLotsofIndependentRandomVariables
6.4.ConditionalProbabilitiesandExpectations
6.4.1.ConditioningwithRespecttoRandomVariables
Notation
References
Index
……
序言 To some extent，it would be accurate to summarize the contents of this book as an intolerably protracted description of what happens when eitherone raises a transition probability matrix P（i…e all entries fP） are non-negative and each row of P sums to 1） to higher and higher powers or oneexponentiates R（P-11，where R is a diagonal mattix With non-negativeentries.Indeed，when it comes right down to it，that is all that is done inthis book.However，I，and others of my ilk，would take offense at such a dismissive characterization of the theory of Markov chains and processes Withvalues in a countable state space，and a primary goal ofmine in writing thisbook Was to convince its readers that our offense would be warranted. The reason why I，and others of my persuasion，refuse to consider the theoryhere as no more than a subset of matrix theory is that to do so is to ignore thepervasive role that probability plays throughout.Namely,probability theoryprovides a model which both motivates and provides a context for what weare doing with these matrices.To Wit.even the term“transition probabilitymatrix”lends meaning to an otherwise rather peculiar set of hypotheses tomake about a matrix.Namely,it suggests that we think of the matfix entry（P） as giving the probability that，in one step，a system in state i will makea transition to state J.Moreover，if we adopt this interpretation for（P）O，then we must interpret the entry（P） of P as the probability ofthe sametransition in steps.Thus，as P is encoding the long time behaviorof a randomly evolving system for which P encodes the one-step behavior，and，as we will see，this interpretation will guide US to an understanding oflim P.In addition，and perhaps even more important，is the rolethat probability plays in bridging the chasm between mathematics and therest of the world.Indeed，it is the probabilistic metaphor which allows one toformulate mathematical models of various phenomena observed in both thenatural and social sciences.Without the language of probability,it is hard toimagine how one would frO about connectin~such phenomena to P.
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