一類隨機過程之乘積的泛函極限定理.pdf

1、浙江大學(xué)理學(xué)院碩士學(xué)位論文一類隨機過程之乘積的泛函極限定理姓名：樓穎申請學(xué)位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導(dǎo)教師：張立新20070501AbstractLet瓦；他≥1)besequenceofrandomvariables，&=∑甄，n≥1Thestudyofpartialsumof‰isverypopularinthelastCenturySuchasthecentrallimittheorythes仕onglawoflarge

2、numbersandthelawofiteratedlogarithmSomescholarshavestudiedtheasymptoticsforproductsofsumsintherecentyearsArnoldandVillasefior(1998)provedthat∑logSknlognn生L——_———一三Nn_oo、／2nwhereNisastandardnormalrandomvariableandsnisthep

3、artialsulnsofexponentialrandomvariableswhosemeanis1RempalaandWesolowski(2002)improvedtheirresultsandgottheasymptoticdistributionofproductsofSUDISofiidpositivesquareintegrablerandomvariablesQi(2003)andQiandLu(2004)extende

4、dthisresulttoagenerallimittheoremcoveringthecasewhentheunderlingdistributionisinthedomainofattractionofastablelawwimindexfromtheinterval【1，2】RempalaandWesolowski(2005)extendedthisresultconsidering咒，t)扭1，，kk=1，2，tobeatria

5、ngulararrayofiidpositivesquareintegrablerandomvariables，andJinandWang(2006)considered％，n≥1)tobeasequenceofnegativelyassociatedidenticallydistributedrandomvariablesThispapermainlyconsidersaboutthefunctionalcentrallimitthe

6、oremandfunc—tionallawofiteratedlogarithmofmartingalesandakindofstationaryergodicstochasticprocessesrelatedtomartingalesWeprovedthetheoremsofthispaperbythesimilarmethodinZhangandWan97SpaperJustasthereferencesmentionedabov

7、e，weuseinvarianceprincipleandthelawofiteratedlogarithmtogetthelimitdistributionInthefirstchapterwewillintroducetheworkswhichsomescholarshavealreadyobtainedInthesecondchapterwewillusetheinvarianceprincipleofmartingalestoo

8、btainthe，functionallimitdistributionofproductsofsumsofmartingalesAtthethirdchapterwewillusetheinvarianceprincipleforthelawofiteratedlogarithmtoobtainfunctionallawofiteratedlogarithmandfunctionalcentrallimittheoremforasta