概率论影印版（第3版）

　　This book is a complete revision of the earlier work Probability which appeared in 1970. While revised so radically and incorporating so much new material as to amount to a new text， it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability， demanding a reasonable but not extensive knowledge of mathematics， and taking the reader to what one might describe as a good intermediate level'. In doing so it attempted to break away from stereotyped applications， and consider applications of a more novel and significant character. The particular novelty of the approach was that expectation was taken as the prime concept， and the concept of expectation axiomatized rather than that of a probability measure. In the preface to the original text of 1970 （reproduced below， together with that to the Russian edition of 1982） I listed what I saw as the advantages of the approach in as unlaboured a fashion as I could. I also took the view that the text rather than the author should persuade， and left the text to speak for itself. It has， indeed， stimulated a steady interest， to the point that Springer-Verlag has now commissioned this complete reworking.本书为英文版。

暂缺《概率论影印版（第3版）》作者简介

PrefacetotheThirdEdition
PrefacetoProbability(1970)
PrefacetotheRussianEditionofProbability(1982)
CHAPTER1
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.AConditionalExpectationasaRandomVariable
4.Conditioningona-Field
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.TheCaseoraDiscreteStateSpace: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.ProcessesofIndependentIncrements
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.Fieldsanda-FieldsofEvents
3.ExtensiononaLinearLattice
4.IntegrableFunctionsofaScalarRandomVariable
5.ExpectationsDerivablefromtheCharacteristicFunction:
WeakConvergence
CHAPTER16
SomeInterestingProcesses
1.InformationTheory:BlockCoding
2.InformationTheory:MoreontheShannonMeasure
3.InformationTheory:SequentialInterrogationandQuestionnaires
4.DynamicOptimization
5.QuantumMechanics:theStaticCase
6.QuantumMechanics:theDynamicCase
References
Index