概率论教程

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