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Invariance principle for integral type functionals

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Abstract

Let {Xnj, n [greater-or-equal, slanted] 1, j[greater-or-equal, slanted]1} be a doubly indexed array of random variables, and let [tau]n= {[tau]n(t), 0 =1} are nondecreasing, have left limits and are right continuous. Let Sni=[Sigma]ik=1Xnk, V2ni =[Sigma]ik=1X2nk,k[greater-or-equal, slanted]1,n[greater-or-equal, slanted]1. Suppose f,fn,n[greater-or-equal, slanted]1, are functions defined on [0,[infinity])x(-[infinity],[infinity]), and define , , 0 [infinity].

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