ON THE ONE-SIDED LOGARITHMIC LAW FOR ARRAYS

1.IntroductionLet{X.,n2l}beasequenceofindependentandidenticallydistributed(i.i.d.)randomvariables.TheHartmanandWintner,sllllawoftheiteratedlogarithmstatesthatifEXI~0andEX7=1Moreover,itisprovedin[2]and[3]that(1)holdsifandonlyifEXI~0andEX7=1.Nowlet{Xnk,k=1,2,''tntn~1,2,'.}beanarrayofi.i.d.randomvariables.FOreveryn21setS.~Z:--,X.k'ThealmostsureconvergenceofSahasbeenstlldiedbyHu,MoriczandTaylor[41,HuandWeb.rls]andQi[6].HuandWeber[5]showedundertheconditionsEXll=0,EX7,=1andEXt,相似文献   

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