On the convergence of series of dependent random variables

2020/06/15 by Mukeru, Safari
#40A05 #60B12 #60G50 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2006.08171

Abstract

Given a sequence (X_n) of symmetrical random variables taking values in a Hilbert space, an interesting open problem is to determine the conditions under which the series ∑_n=1^∞ X_n is almost surely convergent. For independent random variables, it is well-known that if ∑_n=1^∞ 𝔼(‖X_n‖²)

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