| Título: | A Proof of a Conjecture of Bobkov and Houdré |
| Autores: |
Kwapien, S.; Warsaw University Pycia, M.; Warsaw University Schachermayer, W.; University of Vienna |
| Fecha: | 1996-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Gaussian distribution. 60E05, 60E15 |
| Descripción: | 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. |
| Idioma: | No aplica |
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