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Proceedings of the American Mathematical Society

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Subgaussianity is hereditarily determined


Authors: Pandelis Dodos and Konstantinos Tyros
Journal: Proc. Amer. Math. Soc. 148 (2020), 2915-2930
MSC (2010): Primary 46B09, 60E15
DOI: https://doi.org/10.1090/proc/14947
Published electronically: February 18, 2020
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Abstract: Let $ n$ be a positive integer, let $ \boldsymbol {X}=(X_1,\dots ,X_n)$ be a random vector in $ \mathbb{R}^n$ with bounded entries, and let $ (\theta _1,\dots ,\theta _n)$ be a vector in $ \mathbb{R}^n$. We show that the subgaussian behavior of the random variable $ \theta _1 X_1+\dots +\theta _n X_n$ is essentially determined by the subgaussian behavior of the random variables $ \sum _{i\in H} \theta _i X_i$ where $ H$ is a random subset of $ \{1,\dots ,n\}$.


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Pandelis Dodos
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 157 84, Athens, Greece
Email: pdodos@math.uoa.gr

Konstantinos Tyros
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 157 84, Athens, Greece
Email: ktyros@math.uoa.gr

DOI: https://doi.org/10.1090/proc/14947
Keywords: Subgaussian random variable, subgaussian random vector, subvector.
Received by editor(s): April 25, 2019
Received by editor(s) in revised form: October 29, 2019, and November 6, 2019
Published electronically: February 18, 2020
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2020 American Mathematical Society