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Unconditional Convergence of Functional Series in Problems of Probability Theory

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Abstract

We study the unconditional convergence of series in Banach spaces. We consider series of special type (Hadamard series), obtain the condition of their unconditional convergence, and discuss some of their applications. Further, we examine the almost sure unconditional convergence of random series in Banach spaces and, in the case of Gaussian series, we establish the relationship between the almost sure unconditional convergence and the geometry of Banach spaces. We also consider some probabilistic problems related to the convergence of series.

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  1. N. I. Muskhelishvili Institute for Computational Mathematics, Georgian Technical University, Tbilisi, Georgia

    V. V. Kvaratskhelia

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 86, Probability Theory, 2013.

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Kvaratskhelia, V.V. Unconditional Convergence of Functional Series in Problems of Probability Theory. J Math Sci 200, 143–294 (2014). https://doi.org/10.1007/s10958-014-1912-1

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