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A Proof of a Conjecture of Bobkov and Houdré


 
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1. Title Title of document A Proof of a Conjecture of Bobkov and Houdré
 
2. Creator Author's name, affiliation, country S. Kwapien; Warsaw University
 
2. Creator Author's name, affiliation, country M. Pycia; Warsaw University
 
2. Creator Author's name, affiliation, country W. Schachermayer; University of Vienna
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gaussian distribution.
 
3. Subject Subject classification 60E05, 60E15
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 1996-02-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/972
 
10. Identifier Digital Object Identifier 10.1214/ECP.v1-972
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 1
 
12. Language English=en
 
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