On the Convergence of Series of Dependent Random Variables

Safari Mukeru ()
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Safari Mukeru: University of South Africa

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1299-1320

Abstract: Abstract Given a sequence $$(X_n)$$ ( 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 $$\sum _{n=1}^\infty X_n$$ ∑ n = 1 ∞ X n is almost surely convergent. For independent random variables, it is well known that if $$\sum _{n=1}^\infty \mathbb {E}(\Vert X_n\Vert ^2)

Keywords: Random series; Almost sure convergence; $$L^2$$ L 2 -convergence; Hilbert spaces; 60B12; 60G50; 40A05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01018-9

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