Chung Kailai_Elementary Probability Theory英文文献资料

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1、DoobPolyaKolmogorovCramerBorelLevyKeynesFellerContentsPREFACETOTHEFOURTHEDITIONxiPROLOGUETOINTRODUCTIONTOMATHEMATICALFINANCExiii1SET11.1Samplesets11.2Operationswithsets31.3Variousrelations71.4Indicator13Exercises172PROBABILITY202.1Examplesofprobability202.2Definitionandillustratio

2、ns242.3Deductionsfromtheaxioms312.4Independentevents352.5Arithmeticaldensity39Exercises423COUNTING463.1Fundamentalrule463.2Diversewaysofsampling493.3Allocationmodels;binomialcoefficients553.4Howtosolveit62Exercises70viiviiiContents4RANDOMVARIABLES744.1Whatisarandomvariable?744.2How

3、dorandomvariablescomeabout?784.3Distributionandexpectation844.4Integer-valuedrandomvariables904.5Randomvariableswithdensities954.6Generalcase105Exercises109APPENDIX1:BORELFIELDSANDGENERALRANDOMVARIABLES1155CONDITIONINGANDINDEPENDENCE1175.1Examplesofconditioning1175.2Basicformulas

4、1225.3Sequentialsampling1315.4P´olya’surnscheme1365.5Independenceandrelevance1415.6Geneticalmodels152Exercises1576MEAN,VARIANCE,ANDTRANSFORMS1646.1Basicpropertiesofexpectation1646.2Thedensitycase1696.3Multiplicationtheorem;varianceandcovariance1736.4Multinomialdistribution1806.5G

5、eneratingfunctionandthelike187Exercises1957POISSONANDNORMALDISTRIBUTIONS2037.1ModelsforPoissondistribution2037.2Poissonprocess2117.3Frombinomialtonormal2227.4Normaldistribution2297.5Centrallimittheorem2337.6Lawoflargenumbers239Exercises246APPENDIX2:STIRLING’SFORMULAANDDEMOIVRE–LA

6、PLACE’STHEOREM251Contentsix8FROMRANDOMWALKSTOMARKOVCHAINS2548.1Problemsofthewandererorgambler2548.2Limitingschemes2618.3Transitionprobabilities2668.4BasicstructureofMarkovchains2758.5Furtherdevelopments2848.6Steadystate2918.7Windingup(ordown?)303Exercises314APPENDIX3:MARTINGALE32

7、59MEAN-VARIANCEPRICINGMODEL3299.1Aninvestmentsprimer3299.2Assetreturnandrisk3319.3Portfolioallocation3359.4Diversification3369.5Mean-varianceoptimization3379.6Assetreturndistributions3469.7Stableprobabilitydistributions348Exercises351APPENDIX4:PARETOANDSTABLELAWS35510OPTIONPRICING

8、THEORY35910.1Optionsbasics35910.2Arbitra