An Almost Sure Central Limit Theorem for Self-normalized Weighted Sums

(整期优先)网络出版时间:2013-01-11
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LetX,X1,X2,···beasequenceofnondegeneratei.i.d.randomvariableswithzeromeans,whichisinthedomainofattractionofthenormallaw.Let{ani,1≤i≤n,n≥1}beanarrayofrealnumberswithsomesuitableconditions.Inthispaper,weshowthatacentrallimittheoremforself-normalizedweightedsumsholds.WealsodeduceaversionofASCLTforself-normalizedweightedsums.