空間布朗單由局部蔓延導(dǎo)致的占有測度分析.pdf

1、福建師范大學(xué)碩士學(xué)位論文空間布朗單由局部蔓延導(dǎo)致的占有測度分析姓名：倪文清申請學(xué)位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導(dǎo)教師：莊興無林火南2003.4.1ABSTRACTLongafterthetimewhenCiesielskiandTaylorobtainedthelawofiteratedlogarithmofoccupationmeasureofspatialBrownianmotion，Dembo，Peres，RosenandZ

2、eitounimadeamultifractalanalysisofoccupationmeasureofspatialBrownianmo—tion，andgotthemultifractalspectrumoftheoccupationmeasureOntheotherside，therearelesspeoplewhofoCUSontheoccupationmeasureofBrownainsheet，whichcontribut

3、estolessresultsInthispaper，wemainlydiscusstheoccupationmeasureofspatialBrowniansheetwhichcomefromthelocalpropagationofthickpointsonline、)＼，edividethispaperintothreepartsasfollows：Inthefirstpart，weintroducesomepreliminary

4、notationsandbasic1emma、whichareconvenientforlaterdisscussionInthesecondpart，wegiveanotherproofoftheexistenceofBrowniansheetwhichallsamplepathsarecontinuousThisproofusestwo—parameterBorel—Cantellilemmaandmaximuminequality

5、ofBrowniansheetwhichshowsmorecharacteristicinproba—bilitywayAndtheprocessoftheproofiSsimilartothatofsingleparameterBrownianmotionInthelastpart，asthecoreofthispaper，weanalyzetheoccupationmeasureofspatialBrowniansheetwhich

6、comefromthelocalpropagationofthickpointsonlineandobtainthefollowingresult：Supposethat鞏，t)isatwoparameterBrowniansheetinRd(d23)，andthatp△vv’(B(鞏，t，E))denotestheoccupationmeasureofBrowniansheetwhichcomefromthelocalpropagat

7、ionofthickpointsonlineintheintervalAandintheballB(眠，t，￡)，hereweletAdenotestheinterval【po，po2】qo，qo2]foranyPo，qooLetk0=minpo，qo，andqddenotethefirstpositivezerooftileBesselfunctions●一2(z)F0ranya∈(0，辦)，wehaveS10naim㈣ⅢIliras