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Springer.Kyprianou.A.Introductory.Lectures.On.Fluctuations.Of.Levy.Processes.With.Applications.(Springer.2005)(272S)

Springer.Kyprianou.A.Introductory.Lectures.On.Fluctuations.Of.Levy.Processes.With.Applications.(Springer.2005)(272S)

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大小：14.58 MB

页数：272页

时间：2019-03-13

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1、AndreasE.KyprianouIntroductoryLecturesonFluctuationsofL´evyProcesseswithApplicationsJuly29,2005SpringerBerlinHeidelbergNewYorkHongKongLondonMilanParisTokyoPrefaceIn2003IbeganteachingacourseentitledL´evyprocessesontheAmsterdam-Utrechtmastersprogrammeinstochasticsandfinancialmathematics.Quitenaturall

2、y,IwantedtoexposetomystudentsmyowninterestsinL´evypro-cesses.Thatistherolethatcertainsubtlebehaviourconcerningtheirfluctu-ationsexplaindifferenttypesofphenomenaappearinginanumberofclas-sicalmodelsofappliedprobability(asageneralrulethatdoesnotnecessarilyincludemathematicalfinance).Indeed,recentdevelop

3、mentsinthetheoryofL´evyprocesses,inparticularconcerningpathfluctuation,hasofferedtheclar-ityrequiredtorevisitclassicalappliedprobabilitymodelsandimproveonwellestablishedandfundamentalresults.Resultswhichwereinitiallyresponsibleforthepopularityofthemodelsthemselves.WhilstgivingthecourseIwrotesomelect

4、urenoteswhichhavenowma-turedintothistext.Giventheaudienceofstudents,whowereeitherengagedintheir‘afstudeerfase’(equivalenttomastersfortheU.S.orthoseEuropeancountrieswhichhaveengagedinthatsystem)orjuststartingaPh.D.,theselecturenoteswereoriginallywrittenwiththerestrictionthatthemathematicsusedwouldn

5、otsurpassthelevelthattheyshouldinprinciplehavereached.Thatroughlymeansthefollowing.Experiencetothelevelofthirdyearorfourthyearuniversitycoursesdeliveredbyamathematicsdepartmenton-foundationalrealandcomplexanalysis,-elementaryfunctionalanalysis(specificallybasicfactsaboutLpspaces),-measuretheory,int

6、egrationtheoryandmeasuretheoreticprobabilitytheory,-elementsoftheclassicaltheoryofMarkovprocesses,stoppingtimesandtheStrongMarkovProperty,Poissonprocessesandrenewalprocesses,-anunderstandingofBrownianmotionasaMarkovprocessandelementarymartingaletheoryincontinuoustime.Forthemostpartthisaffectedthewa

7、yinwhichthematerialwashandledcomparedtotheclassicaltextsandresearchpapersfromwhichalmostalloftheresultsandargumentsinthistextoriginate.LikewisetheexercisesareVIPrefacepitchedatalevelappropriatetothisaudience.Inde

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