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

作者：Wu, Qunying^*

来源：Chinese Annals of Mathematics Series B, 2012, 33(6): 919-930.

DOI：10.1007/s11401-012-0742-z

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

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.

• 出版日期2012-11
• 单位桂林理工大学