随机过程高级教程：A Second Course in Stochastic Processes (图灵原版数学·统计学系列)

图书标准信息

• 作者 [美]卡林（Karlin S.） 著
• 出版社 人民邮电出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787115191816
• 定价 89.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 542页
• 字数 504千字
• 正文语种 英语
• 丛书 图灵原版数学·统计学系列

【内容简介】

　　本书是人民邮电出版社影印和翻译出版的《随机过程初级教程》的姊妹篇，内容包括马尔可夫链的代数方法、转移概率的比定理及应用、连续时间马尔可夫链、扩散过程、复合随机过程、独立同分布随机变理部分和波动理论、排队过程等很多主题。本书将理论与应用有机地结合在一起，取得了完美的平衡。
　　本书适用而广，可供数学、物理学、生物学、社会学、管理学和其他工程领域的理论研究者和实践者学习。

【作者简介】

　　SamuelKarlin，斯坦福大学荣休教授，国际著名的应用概率学家，美国科学院院士，数理统计学会会士。1987年获冯·诺伊曼奖。在生灭过程中计算平稳分布的Karlin-McGregor定理即以他的名字命名。
　　HowardM.Taylor，康奈尔大学荣休教授，国际著名的应用概率学家。

【目录】

Chapter10　ALGEBRAICMETHODSINMARKOVCHAINS
1.Preliminaria
2.RelationsofEigenvaluesandRecurrenceClaum
3.PeriodicClasses
4.SpecialComputationalMethodsinMarkovChains
5.Examples
6.ApplicationstoCoinTomin
ElementaryProblems
Problermt
Nores
References

Chapter11RATIOTHEoREMSoFTRANSITl0NPROBABILITIESANDAPPLICATl0NS
1.TabooProbabilities
2.RatioTheorems
3.ExistenceofGeneralizedStationaryDistributions
4.InterpretationofGeneralizedStationaryDistributions
5.Regular，Superregular，andSubregularSequencesfor　MarkovChains
6.StoppingRuleProblems
ElementaryProblems
Problems
Notes
References

Chapter12　SUMSOFINDEPENDENTRANDOMVARIABLESASAMARKOVCHAIN
1.RecurrencePropertiesofSumsofIndependentRandomVariables
2.LocalLimitTheorems
3.RightRegularSequencesfortheMarkovChain
4.TheDiscreteRenewalTheorem
ElementaryProblems
Problems
Notes
References

Chapter13　ORDERSTATISTICS，POISSONPROCESSES，AND
APPLICATIONS
1.OrderStatisticsandTheirRelationtoPoissonProcesses
2.TheBallotProblem
3.EmpiricalDistributionFunctions
4.SomeLimitDistributionsforEmpiricalDistributionFunctions
ElementaryProblems
Problems
Notes
References

Chapter14CONTINUOUSTIMEMARKOVCHAINS
1.DifferentiabilityPropertiesofTransitionProbabilities
2.ConservativeProcessesandtheForwardandBackwardDifferentialEquations
3.ConstructionofaContinuousTimeMarkovChainfromItsInfinitesimalParameters
4.StrongMarkovProperty
Problems
Notes
References

Chapter15DIFFUSIONPROCESSES..
1.GeneralDescription
2.ExamplesofDiffusion
3.DifferentialEquationsAssociatedwithCertainFunctionals
4.SomeConcreteCasesoftheFunctionalCalculations
5.TheNatureofBackwardandForwardEquationsandCalculationofStationaryMeasures
6.BoundaryClassificationforRegularDiffusionProcesses
7.SomeFurtherCharacterizationofBoundaryBehavior
8.SomeConstructionsofBoundaryBehaviorofDiffusionProcesses
9.ConditionedDiffusionProcesses
10.SomeNaturalDiffusionModelswithKilling
11.SemigroupFormulationofContinuousTimeMarkovProcesses
12.FurtherTopicsintheSemigroupTheoryofMarkovProcessesandApplicationstoDiffusions
13.TheSpectralRepresentationoftheTransitionDensityforaDiffusion
14.TheConceptofStochasticDifferentialEquations
15.SomeStochasticDifferentialEquationModels
16.APreviewofStochasticDifferentialEquationsandStochasticIntegrals
ElementaryProblems
Problems
Notes
References

Chapter16COMPOUNDINGSTOCHASTICPROCESSES
1.MultidimensionalHomogeneousPoissonProcesses
2.AnApplicationofMultidimensionalPoissonProcessestoAstronomy
3.ImmigrationandPopulationGrowth
4.StochasticModelsofMutationandGrowth
5.One-DimensionalGeometricPopulationGrowth
6.StochasticPopulationGrowthModelinSpaceandTime
7.DeterministicPopulationGrowthwithAgeDistribution
8.ADiscreteAgingModel
9.CompoundPoissonProcesses
ElementaryProblems
Problems
Notes
References

Chapter17FLUCTUATIONTHEORYOFPARTIALSUMSOFINDEPENDENTIDENTICALLYDISTRIBUTEDRANDOMVARIABLES
1.TheStochasticProcessofPartialSums
2.AnEquivalencePrinciple
3.SomeFundamentalIdentitiesofFluctuationTheoryandDirectApplications
4.TheImportantConceptofLadderRandomVariables
5.ProofoftheMainFluctuationTheoryIdentities
6.MoreApplicationsofFluctuationTheory
Problems
Notes
References

Chapter18QUEUEINGPROCESSES
1.GeneralDescription
2.TheSimplestQueueingProcesses(M/M/l)
3.SomeGeneralOne-ServerQueueingModels
4.EmbeddedMarkovChainMethodAppliedtotheQueueingModel(M/GI/l)
5.ExponentialServiceTimes(G/M/1)
6.GammaAmvalDtstnbutlonandGeneralizations(Ek/M/1)
7.ExponentialServicewithsServers(GI/M/s)
8.TheVirtualWaitingTimeandtheBusyPeriod
Problems
Notes
References
MISCELLANEOUSPROBLEMS
Index