# On the Convergence of Some Random Series

### Thomas Mikosch

University of Copenhagen, Denmark

## Abstract

Let $\{ X_n \}$ be a sequence of independent random elements with values in a separable Banach space, $S_n = X_1 + \cdots + X_n$ and $\{a_n\}$ a sequence of nonnegative numbers. There is proved a criterion for the almost sure convergence of the series $\sum a_nS_n$. The special case $a_n = n^{–\alpha}, \alpha > 0$ is also studied.

## Cite this article

Thomas Mikosch, On the Convergence of Some Random Series. Z. Anal. Anwend. 6 (1987), no. 2, pp. 183–187

DOI 10.4171/ZAA/241