Abstract:

Let {X_n, n≥1} be a sequence of i.i.d. positive square integrable random variables with continuous and independent medium tail distribution function. For a fixed constant a>0, T_n(a)=S_n-S_n(a) denoted the trimmed sum, we proved the almost sure central limit theorem for the product of trimmed sums under the general weight by using the limit properties of the trimmed sums and the law of large numbers.

Key words: trimmed sum, almost sure central limit theorem, medium tail distribution, logarithmic average