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

MathSciNet review:
4099780

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**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

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