图书信息

作者简介

内容简介

目录

图书信息

出版社: 世界图书出版公司; 第1版 (2009年4月1日)

外文书名: An Introduction to Markov Processes

平装: 171页

正文语种: 英语

开本: 24

ISBN: 7510004489, 9787510004483

条形码: 9787510004483

尺寸: 22 x 14.6 x 0.8 cm

重量: 240 g

作者简介

作者：(美国) 丹尼尔斯特鲁克 (Strook.D.W.)

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

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