马尔科夫过程导论

马尔科夫过程导论

(美) 丹尼尔斯特鲁克 (Strook,D.W.) , 著

出版社:世界图书出版公司北京公司

年代:2009

定价:25.0

书籍简介:

本书是Springer研究生数学教程第230卷,本书以严格但又很基础的方式讲述了可数状态空间上的马尔科夫过程理论。对于有基本数学背景的工程、经济、物理和生物领域的学生都是很容易学懂的。

书籍目录:

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.RecurrenceofSymmetricRandomWalkinZz

1.2.4.nansienceinZ3

1.3.Exercises

Chapter2Doeblin’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

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.TheQMatrixandKolmogorov’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

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.TheDirichletFo.rmandPoincar4’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.Estimatingλ

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

内容摘要:

  Tosomeextent,itwouldbeaccuratetosummarizethecontentsofthisbookasanintolerablyprotracteddescriptionofwhathappenswheneitheroneraisesatransitionprobabilitymatrixP(i.e.,allentries(P)arenonnegativeandeachrowofPsumsto1)tohigherandhigherpowersoroneexponentiatesR(P-I),whereRisadiagonalmatrixwithnon-negativeentries.Indeed,whenitcomesrightdowntoit,thatisallthatisdoneinthisbook.However,I,andothersofmyilk,wouldtakeoffenseatsuchadismissivecharacterizationofthetheoryofMarkovchainsandprocesseswithvaluesinacountablestatespace,andaprimarygoalofmineinwritingthisbookwastoconvinceitsreadersthatouroffensewouldbewarranted.

书籍规格:

书籍详细信息
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9787510004483
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出版地北京出版单位世界图书出版公司北京公司
版次1版印次1
定价(元)25.0语种英文
尺寸14装帧平装
页数印数 1000

书籍信息归属:

马尔科夫过程导论是世界图书出版公司北京公司于2009.04出版的中图分类号为 O211.62 的主题关于 马尔柯夫过程-研究生-教材-英文 的书籍。