资源描述:
《Brownian motion》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、ThispageintentionallyleftblankBrownianMotionThiseagerlyawaitedtextbookoffersabroadanddeepexpositionofBrownianmotion.Extensivelyclasstested,itleadsthereaderfromthebasicstothelatestresearchinthearea.StartingwiththeconstructionofBrownianmotion,thebookthenproceedstosamplepath
2、propertiessuchascontinuityandnowheredifferentiability.NotionsoffractaldimensionareintroducedearlyandareusedthroughoutthebooktodescribefinepropertiesofBrownianpaths.TherelationofBrownianmotionandrandomwalkisexploredfromseveralviewpoints,includingadevelopmentofthetheoryofBro
3、wnianlocaltimesfromrandomwalkembeddings.Stochasticintegrationisintroducedasatool,andanaccessibletreatmentofthepotentialtheoryofBrownianmotionclearsthepathforanextensivetreatmentofintersectionsofBrownianpaths.AninvestigationofexceptionalpointsontheBrownianpathandanappendix
4、onSLEprocesses,byOdedSchrammandWendelinWerner,leaddirectlytorecentresearchthemes.‘ThissplendidaccountofthemoderntheoryofBrownianmotionputsspecialemphasisonsamplepathpropertiesandconnectionswithharmonicfunctionsandpotentialtheory,withoutomittingsuchimportanttopicsasstochas
5、ticintegration,localtimesorrelationswithrandomwalk.ThemostsignificantpropertiesofBrownianmotionarederivedviapowerfulandelegantmethods.Thisbook,whichfillsagapintheexistingliterature,willbeofinterestbothtothebeginner,fortheclarityofexpositionandthejudiciouschoiceoftopics,andt
6、othespecialist,whowillfindneatapproachestomanyclassicalresultsandtosomemorerecentones.ThisbeautifulbookwillsoonbecomeamustforanybodywhoisinterestedinBrownianmotionanditsapplications.’Jean-Franc¸oisLeGall,UniversiteParis11(Paris-Sud,Orsay)´‘BrownianMotionbyMortersandPeres,a
7、modernandattractiveaccountofoneofthecentraltopics¨ofprobabilitytheory,willservebothasanaccessibleintroductionatthelevelofaMaster’scourseandasaworkofreferenceforfinepropertiesofBrownianpaths.TheuniquefocusofthebookonBrownianmotiongivesitasatisfyingconcretenessandallowsarapi
8、dapproachtosomedeepresults.Theintroductorychapters,besidesprovidingacarefulaccountofthetheory,of