• 概率论教程
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概率论教程

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北京海淀
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作者[德]凯兰克 著

出版社世界图书出版公司

出版时间2012-06

版次1

装帧平装

货号A11

上书时间2024-10-31

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图书标准信息
  • 作者 [德]凯兰克 著
  • 出版社 世界图书出版公司
  • 出版时间 2012-06
  • 版次 1
  • ISBN 9787510044113
  • 定价 79.00元
  • 装帧 平装
  • 开本 24开
  • 纸张 胶版纸
  • 页数 616页
【内容简介】
  《概率论教程》是一部讲述现代概率论及其测度论应用基础的教程,其目标读者是该领域的研究生和相关的科研人员。内容广泛,有许多初级教程不能涉及到得的。理论叙述严谨,独立性强。有关测度的部分和概率的章节相互交织,将概率的抽象性完全呈现出来。此外,还有大量的图片、计算模拟、重要数学家的个人传记和大量的例子。这使得表现形式更加活跃。
【目录】
preface
1basicmeasuretheory
1.1classesofsets
1.2setfunctior
1.3themeasureexteriontheorem
1.4measurablemaps
1.5randomvariables
2independence
2.1independenceofevents
2.2independentrandomvariables
2.3kolmogorov's0-1law
2.4example:percolation
3generatingfunctior
3.1definitionandexamples
3.2poissonapproximation
3.3branchingprocesses
4theintegral
4.1cortructionandsimpleproperties
4.2monotoneconvergenceandfatou'slemma
.4.3lebesgueintegralverusriemannintegral
5momentsandlawsoflargenumber
5.1moments
5.2weaklawoflargenumber
5.3stronglawoflargenumber
5.4speedofconvergenceinthestronglln
5.5thepoissonprocess
6convergencetheorems
6.1almostsureandmeasureconvergence
6.2uniformintegrability
6.3exchangingintegralanddifferentiation
7lp-spacesandtheradon-nikodymtheorem
7.1definitior
7.2inequalitiesandthefischer-riesztheorem
7.3hilbertspaces
7.4lebesgue'sdecompositiontheorem
7.5supplement:signedmeasures
7.6supplement:dualspaces
8conditionalexpectatior
8.1elementaryconditionalprobabilities
8.2conditionalexpectatior
8.3regularconditionaldistribution
9martingales
9.1processes,filtratior,stoppingtimes
9.2martingales
9.3discretestochasticintegral
9.4discretemartingalerepresentationtheoremandthecrrmodel
10optionalsamplingtheorems
10.1doobdecompositionandsquarevariation
10.2optionalsamplingandoptionalstopping
10.3uniformintegrabilityandoptionalsampling
11martingaleconvergencetheoremsandtheirapplicatior
11.1doob'sinequality
11.2martingaleconvergencetheorems
11.3example:branchingprocess
12backwardsmartingalesandexchangeability
12.1exchangeablefamiliesofrandomvariables
12.2backwardsmartingales
12.3definetti'stheorem
13convergenceofmeasures
13.1atopologyprimer
13.2weakandvagueconvergence
13.3prohorov'stheorem
13.4application:afreshlookatdefinetti'stheorem
14probabilitymeasuresonproductspaces
14.1productspaces
14.2finiteproductsandtraritionkernels
14.3kolmogorov'sexteriontheorem
14.4markovsemigroups
15characteristicfunctiorandthecentrallimittheorem
15.1separatingclassesoffunctior
15.2characteristicfunctior:examples
15.3l6vy'scontinuitytheorem
15.4characteristicfunctiorandmoments
15.5thecentrallimittheorem
15.6multidimerionalcentrallimittheorem
16infinitelydivisibledistributior
16.1l6vy-khinchinformula
16.2stabledistributior
17markovchair
17.1definitiorandcortruction
17.2discretemarkovchair:examples
17.3discretemarkovprocessesincontinuoustime
17.4discretemarkovchair:recurrenceandtrarience
17.5application:recurrenceandtrarienceofrandomwalks
17.6invariantdistributior
18convergenceofmarkovchair
18.1periodicityofmarkovchair
18.2couplingandconvergencetheorem
18.3markovchainmontecarlomethod
18.4speedofconvergence
19markovchairandelectricalnetworks
19.1harmonicfunctior
19.2reveriblemarkovchair
19.3finiteelectricalnetworks
19.4recurrenceandtrarience
19.5networkreduction
19.6randomwalkinarandomenvironment
20ergodictheory
20.1definitior
20.2ergodictheorems
20.3examples
20.4application:recurrenceofrandomwalks
20.5mixing
21brownianmotion
21.1continuousverior
21.2cortructionandpathproperties
21.3strongmarkovproperty
21.4supplement:fellerprocesses
21.5cortructionvial2-approximation
21.6thespacec([0,∞))
21.7convergenceofprobabilitymeasuresonc([0,∞))
21.8dorker'stheorem
21.9pathwiseconvergenceofbranchingprocesses
21.10squarevariationandlocalmartingales
22lawoftheiteratedlogarithm
22.literatedlogarithmforthebrownianmotion
22.2skorohod'sembeddingtheorem
22.3hartman-wintnertheorem
23largedeviatior
23.1cramer'stheorem
23.2largedeviatiorprinciple
23.3sanov'stheorem
23.4varadhan'slemmaandfreeenergy
24thepoissonpointprocess
24.1randommeasures
24.2propertiesofthepoissonpointprocess
24.3thepoisson-dirichletdistribution
25theit6integral
25.1it6integralwithrespecttobrownianmotion
25.2it6integralwithrespecttodiffusior
25.3theit6formula
25.4dirichletproblemandbrownianmotion
25.5recurrenceandtrarienceofbrownianmotion
26stochasticdifferentialequatior
26.1strongsolutior
26.2weaksolutiorandthemartingaleproblem
26.3weakuniquenessviaduality
references
notationindex
nameindex
subjectindex
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