概率不等式（英文版）

图书标准信息

• 作者 Zhengyan、Zhidong Bai 著
• 出版社 科学出版社
• 出版时间 2010-09
• 版次 1
• ISBN 9787030255624
• 定价 48.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 181页
• 正文语种 英语

【内容简介】

Inequalityhasbecomeanessentialtoolinmanyareasofmathematicalresearch，forexampleinprobabilityandstatisticswhereitisfrequentlyusedintheproofs.ProbabilityInequalitiescoversinequalitiesrelatedwithevents，distributionfunctions，characteristicfunctions，momentsandrandomvariables（elements）andtheirsum.Thebookshallserveasausefultoolandreferenceforscientistsintheareasofprobabilityandstatistics，andappliedmathematics.

【作者简介】

Prof.ZhengyanLinisafellowoftheInstituteofMathematicalStatisticsandcurrentlyaprofessoratZhejiangUniversity，Hangzhou，China.HeistheprizewinnerofNationalNaturalScienceAwardofChinain1997.
Prof.ZhidongBaiisafellowofTWASandtheInstituteofMathematicalStatistics;heisaprofessorattheNationalUniversityofSingaporeandNortheastNormalUniversity，Changchun，China.

【目录】

Chapter1ElementaryInequalitiesofProbabilitiesofEvents
1.1Inclusion-exclusionFormula
1.2CorollariesoftheInclusion-exclusionFormula
1.3FurtherConsequencesoftheInclusion-exclusionFormula
1.4InequalitiesRelatedtoSymmetricDifference
1.5InequalitiesRelatedtoIndependentEvents
1.6LowerBoundforUnion（Chung-ErdSs）
References

Chapter2InequalitiesRelatedtoCommonlyUsedDistributions
2.1InequalitiesRelatedtotheNormald.f.
2.2SlepianTypeInequalities
2.3AndersonTypeInequalities
2.4Khatri-SidakTypeInequalities
2.5CornerProbabilityofNormalVector
2.6NormalApproximationsofBinomialandPoissonDistributions
References

Chapter3InequalitiesRelatedtoCharacteristicFunctions
3.1InequalitiesRelatedOnlywithc.f
3.2InequalitiesRelatedtoc.f.andd.f.
3.3NormalityApproximationsofc.f.ofIndependentSums
References

Chapter4EstimatesoftheDifferenceofTwoDistributionFunctions
4.1FourierTransformation
4.2Stein-ChenMethod
4.3StieltjesTransformation
References

Chapter5ProbabilityInequalitiesofRandomVariables
5.1InequalitiesRelatedtoTwor.v.s
5.2PerturbationInequality
5.3SymmetrizationInequalities
5.4LevyInequality
5.5BickelInequality
5.6UpperBoundsofTailProbabilitiesofPartialSums
5.7LowerBoundsofTailProbabilitiesofPartialSums
5.8TailProbabilitiesforMaximumPartialSums
5.9TailProbabilitiesforMaximumPartialSums（Continuation）
5.10ReflectionInequalityofTailProbability（HoffmannJorgensen）
5.11ProbabilityofMaximalIncrement（Shao）
5.12MogulskiiMinimalInequality
5.13WilksInequality
References

Chapter6BoundsofProbabilitiesinTermsofMoments
6.1Chebyshev-MarkovTypeInequalities
6.2LowerBounds
6.3SeriesofTailProbabilities
6.4KolmogorovTypeInequalities
6.5GeneralizationofKolmogorovInequalityforaSubmartingale
6.6Renyi-HajekTypeInequalities
6.7ChernoffInequality
6.8FukandNagaevInequality
6.9BurkholderInequality
6.10CompleteConvergenceofPartialSums
References

Chapter7ExponentialTypeEstimatesofProbabilities
7.1EquivalenceofExponentialEstimates
7.2PetrovExponentialInequalities
7.3HoeffdingInequality
7.4BennettInequality
7.5BernsteinInequality
7.6ExponentialBoundsforSumsofBoundedVariables
7.7KolmogorovInequalities
7.8ProkhorovInequality
7.9ExponentialInequalitiesbyCensoring
7.10TailProbabilityofWeightedSums
References

Chapter8MomentInequalitiesRelatedtoOneorTwoVariables
8.1MomentsofTruncation
8.2ExponentialMomentofBoundedVariables
8.3HSlderTypeInequalities
8.4JensenTypeInequalities
8.5DispersionInequalityofCensoredVariables
8.6MonotonicityofMomentsofSums
8.7SymmetrizationMomentInequatilies
8.8KimballInequality
8.9ExponentialMomentofNormalVariable
8.10InequatiliesofNonnegativeVariable
8.11FreedmanInequality
8.12ExponentialMomentofUpperTruncatedVariables
References

Chapter9MomentEstimatesof（Maximumof）SumsofRandomVariables
9.1ElementaryInequalities
9.2MinkowskiTypeInequalities
9.3TheCase1≤r≤2
9.4TheCaser≥2
9.5Jack-knifedVariance
9.6KhintchineInequality
9.7Marcinkiewicz-Zygmund-BurkholderTypeInequalities
9.8SkorokhodInequalities
9.9MomentsofWeightedSums
9.10DoobCrossingInequalities
9.11MomentsofMaximalPartialSums
9.12DoobInequalities
9.13EquivalenceConditionsforMoments
9.14SerfiingInequalities
9.15AverageFillRate
References

Chapter10InequalitiesRelatedtoMixingSequences.
10.1CovarianceEstimatesforMixingSequences
10.2TailProbabilityonα-mixingSequence
10.3Estimatesof4-thMomentonp-mixingSequence
10.4EstimatesofVariancesofIncrementsofp-mixingSequence
10.5Boundsof2+δ-thMomentsofIncrementsofp-mixingSequence
10.6TailProbabilityong-mixingSequence
10.7Boundsof2+δ-thMomentofIncrementsofmixingSequence
10.8ExponentialEstimatesofProbabilityonmixingSequence
References

Chapter11InequalitiesRelatedtoAssociativeVariables
11.1CovarianceofPQDVaralbles
11.2ProbabilityofQuadrantonPA（NA）Sequence
11.3Estimatesofc.f.sonLPQD（LNQD）Sequence
11.4MaximalPartialSumsofPASequence
11.5VarianceofIncrementofLPQDSequence
11.6ExpectationofConvexFunctionofSumofNASequence
11.7Marcinkiewicz-Zygmund-BurkholderInequalityforNASequence
References

Chapter12InequalitiesaboutStochasticProcessesandBanachSpaceValuedRandomVariables
12.1ProbabilityEstimatesofSupremumsofaWienerProcess
12.2ProbabilityEstimateofSupremumofaPoissonProcess
12.3FerniqueInequality
12.4BorellInequality
12.5TailProbabilityofGaussianProcess
12.6TailProbabilityofRandomlySignedIndependentProcesses
12.7TailProbabilityofAdaptiveProcess
12.8TailProbabilityonSubmartingale
12.9TailProbabilityofIndependentSuminB-Space
12.10IsoperimetricInequalities
12，11EhrhardInequality
12.12TailProbabilityofNormalVariableinB-Space
12.13GaussianMeasureonSymmetricConvexSets
12.14EquivalenceofMomentsofB-GaussianVariables
12.15ContractionPrinciple
12.16SymmetrizationInequalitiesinB-Space
12.17DecoupIingInequality
References