Electronic Communications in Probability

Electronic Communications in Probability > Vol. 1 (1996) > Paper 2

A Proof of a Conjecture of Bobkov and Houdré

S. Kwapien, Warsaw University
M. Pycia, Warsaw University
W. Schachermayer, University of Vienna

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

 | X+Y |
 P ( ------- > t ) < P ( | X | > t )
 sqrt 2 = = =

for each t > 0. Does it follow that X has finite second moment (which then easily implies that X is Gaussian)?

Full text: PDF

Pages: 7-10

Published on: February 26, 1996

Bibliography

S. G. Bobkov, C. Houdré, Open Problem, Stochastic Analysis Digest no. 15 (9/15/1995).
S. G. Bobkov, C. Houdré, A characterization of Gaussian measures via the isoperimetric property of half-spaces, preprint.

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Electronic Communications in Probability. ISSN: 1083-589X