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

Let {,;≥1} be a sequence of independent and identically distributed positive random variables with a continuous distribution function , and has a medium tail. Denote =∑=1,∑()==1(−<≤) and 2=∑=1(−)2, where =max1≤≤, ∑=(1/)=1, and >0 is a fixed constant. Under some suitable conditions, we show that (∏[]=1(()/))/∫→exp{0(()/)}[0,1], as →∞, where ()=−() is the trimmed sum and {();≥0} is a standard Wiener process