应用随机过程 概率模型导论（英文版 第11版）

　　《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。

　　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。

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