On the Convergence of Some Random Series

  • Thomas Mikosch

    University of Copenhagen, Denmark


Let {Xn}\{ X_n \} be a sequence of independent random elements with values in a separable Banach space, Sn=X1++XnS_n = X_1 + \cdots + X_n and {an}\{a_n\} a sequence of nonnegative numbers. There is proved a criterion for the almost sure convergence of the series anSn\sum a_nS_n. The special case an=nα,α>0a_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