Translator Disclaimer
1996 A Proof of a Conjecture of Bobkov and Houdré
S. Kwapien, M. Pycia, W. Schachermayer
Author Affiliations +
Electron. Commun. Probab. 1: 7-10 (1996). DOI: 10.1214/ECP.v1-972

Abstract

S. G. Bobkov and C. Houdré recently posed the following question on the Internet (Problem posed in Stochastic Analysis Digest no. 15 (9/15/1995)): Let $X,Y$ be symmetric i.i.d. random variables such that $$P(|X+Y|/2 \geq t) \leq P(|X| \geq t),$$ for each $t>0$. Does it follow that $X$ has finite second moment (which then easily implies that $X$ is Gaussian)? In this note we give an affirmative answer to this problem and present a proof. Using a dierent method K. Oleszkiewicz has found another proof of this conjecture, as well as further related results.

Citation

Download Citation

S. Kwapien. M. Pycia. W. Schachermayer. "A Proof of a Conjecture of Bobkov and Houdré." Electron. Commun. Probab. 1 7 - 10, 1996. https://doi.org/10.1214/ECP.v1-972

Information

Accepted: 26 February 1996; Published: 1996
First available in Project Euclid: 25 January 2016

zbMATH: 0854.60014
MathSciNet: MR1386289
Digital Object Identifier: 10.1214/ECP.v1-972

Subjects:
Primary: 60E05
Secondary: 60E15

JOURNAL ARTICLE
4 PAGES


SHARE
Back to Top