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2020 On almost sure convergence of random variables with finite chaos decomposition
Radosław Adamczak
Electron. J. Probab. 25: 1-28 (2020). DOI: 10.1214/20-EJP538

Abstract

Under mild conditions on a family of independent random variables $(X_{n})$ we prove that almost sure convergence of a sequence of tetrahedral polynomial chaoses of uniformly bounded degrees in the variables $(X_{n})$ implies the almost sure convergence of their homogeneous parts. This generalizes a recent result due to Poly and Zheng obtained under stronger integrability conditions. In particular for i.i.d. sequences we provide a simple necessary and sufficient condition for this property to hold.

We also discuss similar phenomena for sums of multiple Wiener-Itô integrals with respect to Poisson processes, answering a question by Poly and Zheng.

Citation

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Radosław Adamczak. "On almost sure convergence of random variables with finite chaos decomposition." Electron. J. Probab. 25 1 - 28, 2020. https://doi.org/10.1214/20-EJP538

Information

Received: 4 November 2019; Accepted: 22 October 2020; Published: 2020
First available in Project Euclid: 15 December 2020

Digital Object Identifier: 10.1214/20-EJP538

Subjects:
Primary: 60B11, 60F99, 60H05

JOURNAL ARTICLE
28 PAGES


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