A Limit Theorem for Random Products of Trimmed Sums of i.i.d. Random Variables

Abstract EN

Let {X,Xi; i≥1} be a sequence of independent and identically distributed positive random variables with a continuous distribution function F, and F has a medium tail.

Denote Sn=∑i=1nXi,Sn(a)=∑i=1nXiI(Mn-a0 is a fixed constant.

Under some suitable conditions, we show that (∏k=1[nt](Tk(a)/μk))μ/Vn→dexp{∫0t(W(x)/x)dx} in D[0,1], as n→∞, where Tk(a)=Sk-Sk(a) is the trimmed sum and {W(t);t≥0} is a standard Wiener process.