片断：
Theapplicationofprobabilitytheorytogamesofchanceisanobviousone.
However,thereareapplicationsinscienceandtechnologywhicharejustas
cleancut.Asexamples,wecanquotethegeneticmechanismofMendelian
inheritance(Sections5.5and9.2),theoperationofatelephoneexchange
(Section10.4)orthedecayofradioactivemolecules(Section10.4).Inallthese
casesonecanmakevaluableprogresswithasimplemodel,althoughitisonly
fairtoaddthatadeeperstudywilldemandsomethingmorecomplicated.
Ingeneral,thephysicalsciencesprovidearichsourc

Contents
PrefacetotheThirdEdition
PrefacetoProbability(1970)
PrefacetotheRussianEditionofProbability(1982)
CHAPTERl
Uncertainty,IntuitionandExpectation
1.IdeasandExamples
2.TheEmpiricalBasis
3.AveragesoveraFinitePopulation
4.RepeatedSampling:Expectation
5.MoreonSampleSpacesandVariables
6.IdealandActualExperiments:Observables
CHAPTER2
Expectation
1.RandomVariables
2.AxiomsfortheExpectationOperator
3.Events:Probability
4.SomeExamplesofanExpectation
5.Moments
6.Applications:OptimizationProblems
7.EquiprobableOutcomes:SampleSurveys
8.Applications:LeastSquareEstimationofRandomVariables
9.SomeImplicationsoftheAxioms
CHAPTER3
Probability
1.Events,SetsandIndicators
2.ProbabilityMeasure
3.ExpectationasaProbabilityIntegral
4.SomeHistory
5.SubjectiveProbability
CHAPTER4
SomeBasicModels
1.AModelofSpatialDistribution
2.TheMultinomial,Binomial,PoissonandGeometricDistributions
3.Independence
4.ProbabilityGeneratingFunctions
5.TheSt.PetersburgParadox
6.Matching,andOtherCombinatorialProblems
7.Conditioning
8.VariablesontheContinuum:theExponentialand
GammaDistributions
CHAPTER5
Conditioning
1.ConditionalExpectation
2.ConditionalProbability
3.AConditionalExpectationasaRandomVanable
4.ConditioningonaField
5.Independence
6.StatisticalDecisionTheory
7.InformationTransmission
8.AcceptanceSampling
CHAPTER6
ApplicationsoftheIndependenceConcept
1.RenewalProcesses
2.RecurrentEvents:RegenerationPoints
3.AResultinStatisticalMechanics:theGibbsDistribution
4.BranchingProcesses
CHAPTER7
TheTwoBasicLimitTheorems
1.ConvergenceinDistribution(WeakConvergence)
2.PropertiesoftheCharacteristicFunction
3.TheLawofLargeNumbers
4.NormalConvergence(theCentralLimitTheorem)
5.TheNormalDistribution
CHAPTER8
ContinuousRandomVariablesandTheirTransformations
1.DistributionswithaDensity
2.FunctionsofRandomVariables
3.ConditionalDensities
CHAPTER9
MarkovProcessesinDiscreteTime
1.StochasticProcessesandtheMarkovProperty
2.TheCaseofaDiscreteStateSpace:theKolmogorovEquations
3.SomeExamples:Ruin,SurvivalandRuns
4.BirthandDeathProcesses:DetailedBalance
5.SomeExamplesWeShouldLiketoDefer
6.RandomWalks,RandomStoppingandRuin
7.AuguriesofMartingales
8.RecurrenceandEquilibrium
9.RecurrenceandDimension
CHAPTER10
MarkovProcessesinContinuousTime
1.TheMarkovPropertyinContinuousTime
2.TheCaseofaDiscreteStateSpace
3.ThePoissonProcess
4.BirthandDeathProcesses
5.ProcessesonNondiscreteStateSpaces
6.TheFilingProblem
7.SomeContinuous-TimeMartingales
8.StationarityandReversibility
9.TheEhrenfestModel
10.ProcessesoflndependentIncrements
11.BrownianMotion:DiffusionProcesses
12.FirstPassageandRecurrenceforBrownianMotion
CHAPTER11
Second-OrderTheory
1.BacktoL2
2.LinearLeastSquareApproximation
3.Projection:Innovation
4.TheGauss-MarkovTheorem
5.TheConvergenceofLinearLeastSquareEstimates
6.DirectandMutualMeanSquareConvergence
7.ConditionalExpectationsasLeastSquareEstimates:
MartingaleConvergence
CHAPTER12
ConsistencyandExtension:theFinite-DimensionalCase
1.TheIssues
2.ConvexSets
3.TheConsistencyConditionforExpectationValues
4.TheExtensionofExpectationValues
5.ExamplesofExtension
6.DependenceInformation:ChernoffBounds
CHAPTER13
StochasticConvergence
1.TheCharacterizationofConvergence
2.TypesofConvergence
3.SomeConsequences
4.ConvergenceinrthMean
CHAPTER14
Martingales
1.TheMartingaleProperty
2.Kolmogorov'sInequality:theLawofLargeNumbers
3.MartingaleConvergence:Applications
4.TheOptionalStoppingTheorem
5.ExamplesofStoppedMartingales
CHAPTER15
Extension:ExamplesoftheInfinite-DimensionalCase
1.GeneralitiesontheInfinite-DimensionalCase
2.FieldsandFieldsofEvents
3.ExtensiononaLinearLattice
4.IntegrableFunctionsofaScalarRandomVariable
5.ExpectationsDerivablefromtheCharacteristicFunction:
WeakConvergence
CHAPTER16
SomeInterestingProcesses
1.InformationTheory:BlockCoding
2.InformationTheory:MoreontheShannonMeasure
3.InfonnationTheory:SequentialInterrogationandQuestionnaires
4.DynamicOptimization
5.QuantumMechanics:theStaticCase
6.QuantumMechanics:theDynamicCase
References
Index