《应用随机过程概率模型导论》是国际知名统计学家Sheldon M. Ross所著的关于基础概率理论和随机过程的经典教材，被加州大学伯克利分校、哥伦比亚大学、普度大学、密歇根大学、俄勒冈州立大学、华盛顿大学等众多国外知名大学所采用。
与其他随机过程教材相比，本书非常强调实践性，内含极其丰富的例子和习题，涵盖了众多学科的各种应用。作者富于启发而又不失严密性的叙述方式，有助于使读者建立概率思维方式，培养对概率理论、随机过程的直观感觉。对那些需要将概率理论应用于精算学、计算机科学、管理学和社会科学的读者而言，本书是一本极好的教材或参考书。
第11版新增大量例子和习题，还对连续时间的马尔可夫链、漂移布朗运动等内容做了修订，更加注重强化读者的概率直观。

内容简介

　　《应用随机过程概率模型导论（英文版第11版）》是一部经典的随机过程著作，叙述深入浅出、涉及面广。主要内容有随机变量、条件期望、马尔可夫链、指数分布、泊松过程、平稳过程、更新理论及排队论等，也包括了随机过程在物理、生物、运筹、网络、遗传、经济、保险、金融及可靠性中的应用。特别是有关随机模拟的内容，给随机系统运行的模拟计算提供了有力的工具。最新版还增加了不带左跳的随机徘徊和生灭排队模型等内容。本书约有700道习题，其中带星号的习题还提供了解答。

　　《应用随机过程概率模型导论（英文版第11版）》可作为概率论与数理统计、计算机科学、保险学、物理学、社会科学、生命科学、管理科学与工程学等专业随机过程基础课教材。

作者简介

　　Sheldon M. Ross，国际知名概率与统计学家，南加州大学工业工程与运筹系系主任。1968年博士毕业于斯坦福大学统计系，曾在加州大学伯克利分校任教多年。研究领域包括：随机模型、仿真模拟、统计分析、金融数学等。Ross教授著述颇丰，他的多种畅销数学和统计教材均产生了世界性的影响，如《概率论基础教程（第8版）》等。

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精彩书评

　　★本书的一大特色是实例丰富，内容涉及多个学科，尤其是精算学……相信任何有上进心的读者都会对此爱不释手。”
　　——JeanLeMaire，宾夕法尼亚大学沃顿商学院

　　★“书中的例子和习题非常出色，作者不仅提供了非常基本的例子，以阐述基础概念和公式，还从尽可能多的学科中提炼出许多较高级的实例，极具参考价值。”
　　——MattCarlton，加州州立理工大学（CalPoly）

1IntroductiontoProbabilityTheory
1.1Introduction
1.2SampleSpaceandEvents
1.3ProbabilitiesDefinedonEvents
1.4ConditionalProbabilities
1.5IndependentEvents
1.6Bayes'Formula
Exercises
References
2RandomVariables
2.1RandomVariables
2.2DiscreteRandomVariables
2.2.1TheBernoulliRandomVariable
2.2.2TheBinomialRandomVariable
2.2.3TheGeometricRandomVariable
2.2.4ThePoissonRandomVariable
2.3ContinuousRandomVariables
2.3.1TheUniformRandomVariable
2.3.2ExponentialRandomVariables
2.3.3GammaRandomVariables
2.3.4NormalRandomVariables
2.4ExpectationofaRandomVariable
2.4.1TheDiscreteCase
2.4.2TheContinuousCase
2.4.3ExpectationofaFunctionofaRandomVariable
2.5JointlyDistributedRandomVariables
2.5.1JointDistributionFunctions
2.5.2IndependentRandomVariables
2.5.3CovarianceandVarianceofSumsofRandomVariables
2.5.4JointProbabilityDistributionofFunctionsofRandomVariables
2.6MomentGeneratingFunctions
2.6.1TheJointDistributionoftheSampleMeanandSampleVariancefromaNormalPopulation
2.7TheDistributionoftheNumberofEventsthatOccur
2.8LimitTheorems
2.9StochasticProcesses
Exercises
References
3ConditionalProbabilityandConditionalExpectation
3.1Introduction
3.2TheDiscreteCase
3.3TheContinuousCase
3.4ComputingExpectationsbyConditioning
3.4.1ComputingVariancesbyConditioning
3.5ComputingProbabilitiesbyConditioning
3.6SomeApplications
3.6.1AListModel
3.6.2ARandomGraph
3.6.3UniformPriors,Polya'sUrnModel,andBose-EinsteinStatistics
3.6.4MeanTimeforPatterns
3.6.5Thek-RecordValuesofDiscreteRandomVariables
3.6.6LeftSkipFreeRandomWalks
3.7AnIdentityforCompoundRandomVariables
3.7.1PoissonCompoundingDistribution
3.7.2BinomialCompoundingDistribution
3.7.3ACompoundingDistributionRelatedtotheNegativeBinomial
Exercises
4MarkovChains
4.1Introduction
4.2Chapman-KolmogorovEquations
4.3ClassificationofStates
4.4Long-RunProportionsandLimitingProbabilities
4.4.1LimitingProbabilities
4.5SomeApplications
4.5.1TheGambler'sRuinProblem
4.5.2AModelforAlgorithmicEfficiency
4.5.3UsingaRandomWalktoAnalyzeaProbabilisticAlgorithmfortheSatisfiabilityProblem
4.6MeanTimeSpentinTransientStates
4.7BranchingProcesses
4.8TimeReversibleMarkovChains
4.9MarkovChainMonteCarloMethods
4.10MarkovDecisionProcesses
4.11HiddenMarkovChains
4.11.1PredictingtheStates
Exercises
References
5TheExponentialDistributionandthePoissonProcess
5.1Introduction
5.2TheExponentialDistribution
5.2.1Definition
5.2.2PropertiesoftheExponentialDistribution
5.2.3FurtherPropertiesoftheExponentialDistribution
5.2.4ConvolutionsofExponentialRandomVariables
5.3ThePoissonProcess
5.3.1CountingProcesses
5.3.2DefinitionofthePoissonProcess
5.3.3InterarrivalandWaitingTimeDistributions
5.3.4FurtherPropertiesofPoissonProcesses
5.3.5ConditionalDistributionoftheArrivalTimes
5.3.6EstimatingSoftwareReliability
5.4GeneralizationsofthePoissonProcess
5.4.1NonhomogeneousPoissonProcess
5.4.2CompoundPoissonProcess
5.4.3ConditionalorMixedPoissonProcesses
5.5RandomIntensityFunctionsandHawkesProcesses
Exercises
References
6Continuous-TimeMarkovChains
6.1Introduction
6.2Continuous-TimeMarkovChains
6.3BirthandDeathProcesses
6.4TheTransitionProbabilityFunctionPij(t)
6.5LimitingProbabilities
6.6TimeReversibility
6.7TheReversedChain
6.8Uniformization
6.9ComputingtheTransitionProbabilities
Exercises
References
7RenewalTheoryandItsApplications
7.1Introduction
7.2DistributionofN(t)
7.3LimitTheoremsandTheirApplications
7.4RenewalRewardProcesses
7.5RegenerativeProcesses
7.5.1AlternatingRenewalProcesses
7.6Semi-MarkovProcesses
7.7TheInspectionParadox
7.8ComputingtheRenewalFunction
7.9ApplicationstoPatterns
7.9.1PatternsofDiscreteRandomVariables
7.9.2TheExpectedTimetoaMaximalRunofDistinctValues
7.9.3IncreasingRunsofContinuousRandomVariables
7.10TheInsuranceRuinProblem
Exercises
References
8QueueingTheory
8.1Introduction
8.2Preliminaries
8.2.1CostEquations
8.2.2Steady-StateProbabilities
8.3ExponentialModels
8.3.1ASingle-ServerExponentialQueueingSystem
8.3.2ASingle-ServerExponentialQueueingSystemHavingFiniteCapacity
8.3.3BirthandDeathQueueingModels
8.3.4AShoeShineShop
8.3.5AQueueingSystemwithBulkService
8.4NetworkofQueues
8.4.1OpenSystems
8.4.2ClosedSystems
8.5TheSystemM/G/
8.5.1Preliminaries:WorkandAnotherCostIdentity
8.5.2ApplicationofWorktoM/G/
8.5.3BusyPeriods
8.6VariationsontheM/G/
8.6.1TheM/G/1withRandom-SizedBatchArrivals
8.6.2PriorityQueues
8.6.3AnM/G/1OptimizationExample
8.6.4TheM/G/1QueuewithServerBreakdown
8.7TheModelG/M/
8.7.1TheG/M/1BusyandIdlePeriods
8.8AFiniteSourceModel
8.9MultiserverQueues
8.9.1Erlang'sLossSystem
8.9.2TheM/M/kQueue
8.9.3TheG/M/kQueue
8.9.4TheM/G/kQueue
Exercises
References
9ReliabilityTheory
9.1Introduction
9.2StructureFunctions
9.2.MinimalPathandMinimalCutSets
9.3ReliabilityofSystemsofIndependentComponents
9.4BoundsontheReliabilityFunction
9.4.1MethodofInclusionandExclusion
9.4.2SecondMethodforObtainingBoundsonr(p)
9.5SystemLifeasaFunctionofComponentLives
9.6ExpectedSystemLifetime
9.6.1AnUpperBoundontheExpectedLifeofaParallelSystem
9.7SystemswithRepair
9.7.1ASeriesModelwithSuspendedAnimation
Exercises
References
10BrownianMotionandStationaryProcesses
10.1BrownianMotion
10.2HittingTimes,MaximumVariable,andtheGambler'sRuinProblem
10.3VariationsonBrownianMotion
10.3.1BrownianMotionwithDrift
10.3.2GeometricBrownianMotion
10.4PricingStockOptions
10.4.1AnExampleinOptionsPricing
10.4.2TheArbitrageTheorem
10.4.3TheBlack-ScholesOptionPricingFormula
10.5TheMaximumofBrownianMotionwithDrift
10.6WhiteNoise
10.7GaussianProcesses
10.8StationaryandWeaklyStationaryProcesses
10.9HarmonicAnalysisofWeaklyStationaryProcesses
Exercises
References
11Simulation
11.1Introduction
11.2GeneralTechniquesforSimulatingContinuousRandomVariables
11.2.1TheInverseTransformationMethod
11.2.2TheRejectionMethod
11.2.TheHazardRateMethod
11.3SpecialTechniquesforSimulatingContinuousRandomVariables
11.3.1TheNormalDistribution
11.3.2TheGammaDistribution
11.3.3TheChi-SquaredDistribution
11.3.4TheBeta(n,m)Distribution
11.3.5TheExponentialDistribution-TheVonNeumannAlgorithm
11.4SimulatingfromDiscreteDistributions
11.4.1TheAliasMethod
11.5StochasticProcesses
11.5.1SimulatingaNonhomogeneousPoissonProcess
11.5.2SimulatingaTwo-DimensionalPoissonProcess
11.6VarianceReductionTechniques
11.6.1UseofAntitheticVariables
11.6.2VarianceReductionbyConditioning
11.6.3ControlVariates
11.6.4ImportanceSampling
11.7DeterminingtheNumberofRuns
11.8GeneratingfromtheStationaryDistributionofaMarkovChain
11.8.1CouplingfromthePast
11.8.2AnotherApproach
Exercises
References
Appendix:SolutionstoStarredExercises
Index