RUC property for chaos of random variables in the uniform norm
EDN: RXOTNQ
Abstract
Let $X=\{X_k\}_{k=1}^\infty$ be a sequence of independent symmetric bounded random variables. This paper investigates systems of the form $\{X_iX_j\}_{i<j}$, $\{X_i X_j X_k\}_{i<j<k},\ldots$, finite unions of such systems, and systems close to them, in the space $L_\infty$ of bounded random variables. Series over such systems do not hold the property of unconditionality: the convergence of the series depends on the ordering of the terms. At the same time, as we demonstrate in the paper, such systems posess a very close property of random unconditional convergence (or RUC-property).
Keywords
uniform norm,
random unconditional convergence (RUC),
Banach spaces geometry,
Rademacher chaos,
polynomial chaos,
symmetric random variables
Supporting agencies: The work was supported by the State Research Programme “Convergence–2025” of the National Academy of Sciences of Belarus (assignment 1.3.05)
About the Authors
P. A. Slinyakov
Institute of Mathematics of the National Academy of Sciences of Belarus; Belarusian State University
Belarus
Belarus
Minsk
K. V. Lykov
Institute of Mathematics of the National Academy of Sciences of Belarus; Belarusian State University
Belarus
Belarus
Minsk
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Slinyakov P.A., Lykov K.V. RUC property for chaos of random variables in the uniform norm. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(2):54-72. EDN: RXOTNQ
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