A simple proof for the continuity of infinite convolutions of binary random variables

Janos Galambos and Imre Kátai

Statistics & Probability Letters, 1989, vol. 7, issue 5, 369-370

Abstract: Let Xj, j [greater-or-equal, slanted] 1, be independent random variables taking the values aj [greater-or-equal, slanted] bj with distribution pj = P(Xj = aj) = 1 - P(Xj = bj). Assume that the infinite series U = [Sigma]Xj is (a.s.) convergent. We give a simple proof for Lévy's theorem on the continuity of the distribution function F(x) of U.

Keywords: binary; random; variables; convergent; infinite; convolution; continuity; of; the; limiting; distribution (search for similar items in EconPapers)
Date: 1989
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