概率论入门

图书标准信息

• 作者 S.I.雷斯尼克（Sidney I. Resnick） 著
• 出版社 世界图书出版公司
• 出版时间 2013-05
• 版次 1
• ISBN 9787510058271
• 定价 69.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 453页
• 正文语种 英语

【内容简介】

　　《概率论入门》是一部十分经典的概率论教程。1999年初版，2001年第2次重印，2003年第3次重印，同年第4次重印，2005年第5次重印，受欢迎程度可见一斑。大多数概率论书籍是写给数学家看的，漂亮的数学材料是吸引读者的一大亮点；相反地，《概率论入门》目标读者是数学及非数学专业的研究生，帮助那些在统计、应用概率论、生物、运筹学、数学金融和工程研究中需要深入了解高等概率论的所有人员。

【目录】

preface
1setsandevents
1.1introduction
1.2basicsettheory
1.2.1indicatorfunctions
1.3limitsofsets
1.4monotonesequences
1.5setoperationsandclosure
1.5.1examples
1.6thea-fieldgeneratedbyagivenclassc
1.7bore1setsontherealline
1.8comparingborelsets
1.9exercises

2probabilityspaces
2.1basicdefinitionsandproperties
2.2moreonclosure
2.2.1dynkin'stheorem
2.2.2proofofdynkin'stheorem
2.3twoconstructions
2.4constructionsofprobabilityspaces
2.4.1generalconstructionofaprobabilitymodel
2.4.2proofofthesecondextensiontheorem
2.5measureconstructions
2.5.1lebesguemeasureon（0，1）
2.5.2constructionofaprobabilitymeasureonrwithgivendistributionfunctionf（x）
2.6exercises

3randomvariables，elements，andmeasurablemaps
3.1inversemaps
3.2measurablemaps，randomelements，inducedprobabilitymeasures
3.2.1composition
3.2.2randomelementsofmetricspaces
3.2.3measurabilityandcontinuity
3.2.4measurabilityandlimits
3.3σ-fieldsgeneratedbymaps
3.4exercises

4independence
4.1basicdefinitions
4.2independentrandomvariables
4.3twoexamplesofindependence
4.3.1records，ranks，renyitheorem
4.3.2dyadicexpansionsofuniformrandomnumbers
4.4moreonindependence：groupings
4.5independence，zero-onelaws，borel-cantellilemma
4.5.1borel-cantellilemma
4.5.2borelzero-onelaw
4.5.3kolmogorovzero-onelaw
4.6exercises

5integrationandexpectation
5.1preparationforintegration
5.1.1simplefunctions
5.1.2measurabilityandsimplefunctions
5.2expectationandintegration
5.2.1expectationofsimplefunctions
5.2.2extensionofthedefinition
5.2.3basicpropertiesofexpectation
5.3limitsandintegrals
5.4indefiniteintegrals
5.5thetransformationtheoremanddensities
5.5.1expectationisalwaysanintegralonr
5.5.2densities
5.6theriemannvslebesgueintegral
5.7productspaces
5.8probabilitymeasuresonproductspaces
5.9fubini'stheorem
5.10exercises

6convergenceconcepts
6.1almostsureconvergence
6.2convergenceinprobability
6.2.1statisticalterminology
6.3connectionsbetweena.s.andj.p.convergence
6.4quantileestimation
6.5lpconvergence
6.5.1uniformintegrability
6.5.2interlude：areviewofinequalities
6.6moreonlpconvergence
6.7exercises

7lawsoflargenumbersandsumsofindependentrandomvariables
7.1truncationandequivalence
7.2ageneralweaklawoflargenumbers
7.3almostsureconvergenceofsumsofindependentrandomvariables
7.4stronglawsoflargenumbers
7.4.1twoexamples
7.5thestronglawoflargenumbersforlidsequences
7.5.1twoapplicationsoftheslln
7.6thekolmogorovthreeseriestheorem
7.6.1necessityofthekolmogorovthreeseriestheorem
7.7exercises

8convergenceindistribution
8.1basicdefinitions
8.2scheff6'slemma
8.2.1scheff6'slemmaandorderstatistics
8.3thebabyskorohodtheorem
8.3.1thedeltamethod
8.4weakconvergenceequivalences；portmanteautheorem
8.5morerelationsamongmodesofconvergence
8.6newconvergencesfromold
8.6.1example：thecentrallimittheoremform-dependentrandomvariables
8.7theconvergencetotypestheorem
8.7.1applicationofconvergencetotypes：limitdistributionsforextremes
8.8exercises

9characteristicfunctionsandthecentrallimittheorem
9.1reviewofmomentgeneratingfunctionsandthecentrallimittheorem
9.2characteristicfunctions：definitionandfirstproperties.
9.3expansions
9.3.1expansionofeix
9.4momentsandderivatives
9.5twobigtheorems：uniquenessandcontinuity
9.6theselectiontheorem，tightness，andprohorov'stheorem
9.6.1theselectiontheorem
9.6.2tightness，relativecompactness，andprohorov'stheorem
9.6.3proofofthecontinuitytheorem
9.7theclassicalcltforiidrandomvariables
9.8thelindeberg-fellerclt
9.9exercises

10martingales
10.1preludetoconditionalexpectation：theradon-nikodymtheorem
10.2definitionofconditionalexpectation
10.3propertiesofconditionalexpectation
10.4martingales
10.5examplesofmartingales
10.6connectionsbetweenmartingalesandsubmartingales
10.6.1doob'sdecomposition
10.7stoppingtimes
10.8positivesupermartingales
10.8.1operationsonsupermartingales
10.8.2upcrossings
10.8.3boundednessproperties
10.8.4convergenceofpositivesupermartingales
10.8.5closure
10.8.6stoppingsupermartingales
10.9examples
10.9.1gambler'sruin
10.9.2branchingprocesses
10.9.3somedifferentiationtheory
10.10martingaleandsubmartingaleconvergence
10.10.1krickebergdecomposition
10.10.2doob's（sub）martingaleconvergencetheorem
10.11regularityandclosure
10.12regularityandstopping
10.13stoppingtheorems
10.14wald'sidentityandrandomwalks
10.14.1thebasicmartingales
10.14.2regularstoppingtimes
10.14.3examplesofintegrablestoppingtimes
10.14.4thesimplerandomwalk
10.15reversedmartingales
10.16fundamentaltheoremsofmathematicalfinance
10.16.1asimplemarketmodel
10.16.2admissiblestrategiesandarbitrage
10.16.3arbitrageandmartingales
10.16.4completemarkets
10.16.5optionpricing
10.17exercises
references
index