An improved result in almost sure central limit theory for products of partial sums with stable distribution

Abstract

Consider a sequence of i.i.d. positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1, 2]. A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan. In a sense, our results reach the optimal form.

Keywords

Almost sure central limit theorem / Product of partial sums / Stable distribution

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