Abstract:

Let {Xn,n≥1} be a sequence of i.i.d., positive sq
uare integrable random variables with continuous medium tailed distribution func
tion. For a fixed constant a>0, let Sn=∑〖DD(〗n〖〗i=1〖DD)〗Xi, M
n=max〖DD(〗〖〗1≤i≤n〖DD)〗 Xi, Sn(a)=∑〖DD(〗n〖〗i=1〖DD)〗X
iI{Mn-a  the weak convergence theorem and continuous mapping theorem, we proved the
 invariance principle for the product of trimmed sums.

Key words: trimmed sums, invariance principle, medium tail distribution, independent and identically distributed (i.i.d.)