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Zeitschrift für Analysis und ihre Anwendungen


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Volume 6, Issue 2, 1987, pp. 183–187
DOI: 10.4171/ZAA/241

Published online: 1987-04-30

On the Convergence of Some Random Series

Thomas Mikosch[1]

(1) University of Copenhagen, Denmark

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.

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Mikosch Thomas: On the Convergence of Some Random Series. Z. Anal. Anwend. 6 (1987), 183-187. doi: 10.4171/ZAA/241