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[美] 钟开莱 著 / 世界图书出版公司 / 2010-01 / 平装
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优惠 满包邮
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初等概率论(第4版)
本书是一部介绍概率论及其应用的入门教程。其原始版本面世已经有30余年,但仍然是本科一二年级的经典概率教程。在第4版中增加了两章讲述应用和数学金融。传承前面版本详细、严谨的风格,讲述了有价证券和期货理论的基本知识。书中用最初等的方法讲述了概率测度、随机变量、分布以及期望等基本概念。离散和连续的案例都有所涉及,在讲述后者的时候运用了微积分知识。配以大量的典型例子重点讲述概率推理,集中介绍了组合问题、Poison过程、随机漫步、遗传模型和Markov链。每章末都附有习题及其解答。目次:集合;概率;计数;随机变量;附录。
读者对象:数学专业的本科生以及广大概率论爱好者。
PREFACETOTHEFOURTHEDITIONPROLOGUETOINTRODUCTIONTOMATHEMATICALFINANCE1SET1.1Samplesets1.2Operationswithsets1.3Variousrelations1.4IndicatorExercises2PROBABILITY2.1Examplesofprobability2.2Definitionandillustrations2.3Deductionsfromtheaxioms2.4Independentevents2.5ArithmeticaldensityExercises3COUNTING3.1Fundamentalrule3.2Diversewaysofsampling3.3Allocationmodels;binomialcoefficients3.4HowtosolveitExercises4RANDOMVARIABLES4.1Whatisarandomvariable?4.2Howdorandomvariablescomeabout?4.3Distributionandexpectation4.4Integer-valuedrandomvariables4.5Randomvariableswithdensities4.6GeneralcaseExercisesAPPENDIX1:BORELFIELDSANDGENERALRANDOMVARIABLES5CONDITIONINGANDINDEPENDENCE5.1Examplesofconditioning5.2Basicformulas5.3Sequentialsampling5.4P61yasurnscheme5.5Independenceandrelevance5.6GeneticalmodelsExercises6MEAN,VARIANCE,ANDTRANSFORMS6.1Basicpropertiesofexpectation6.2Thedensitycase6.3Multiplicationtheorem;varianceandcovariance6.4Multinomialdistribution6.5GeneratingfunctionandthelikeExercises7POISSONANDNORMALDISTRIBUTIONS7.1ModelsforPoissondistribution7.2Poissonprocess7.3Frombinomialtonormal7.4Normaldistribution7.5Centrallimittheorem7.6LawoflargenumbersExercisesAPPENDIX2:STIRLINGSFORMULAANDDEMOIVRE-LAPLACESTHEOREM8FROMRANDOMWALKSTOMARKOVCHAINS8.1Problemsofthewandererorgambler8.2Limitingschemes8.3Transitionprobabilities8.4BasicstructureofMarkovchains8.5Furtherdevelopments8.6Steadystate8.7Windingup(ordown?)ExercisesAPPENDIX3:MARTINGALE9MEAN-VARIANCEPRICINGMODEL9.1Aninvestmentsprimer9.2Assetreturnandrisk9.3Portfolioallocation9.4Diversification9.5Mean-varianceoptimization9.6Assetreturndistributions9.7StableprobabilitydistributionsExercisesAPPENDIX4:PARETOANDSTABLELAWS10OPTIONPRICINGTHEORY10.1Optionsbasics10.2Arbitrage-freepricing:1-periodmodel10.3Arbitrage-freepricing:N-periodmodel10.4FundamentalassetpricingtheoremsExercisesGENERALREFERENCESANSWERSTOPROBLEMSVALUESOFTHESTANDARDNORMALDISTRIBUTIONFUNCTIONINDEX
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