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| HAL: hal-00666733, version 1 |
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| A counter-example to the Cantelli conjecture |
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| Victor Kleptsyn 1Aline Kurtzmann 2 |
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| (2012-02-03) |
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| In this paper, we construct a counter-example to a question by Cantelli, asking whether there exists a non-constant positive measurable function $\varphi$ such that for i.i.d. r.v. $X,Y$ of law $\mN(0,1)$, the r.v. $X+\varphi(X)\cdot Y$ is also Gaussian. For the construction that we propose, we introduce a new tool, the Brownian mass transport: the mass is transported by Brownian particles that are stopped in a specific way. This transport seems to be interesting by itself, turning out to be related to the Skorokhod and Stefan problems. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| Géométrie analytique Probabilités et statistiques |
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| Subject | : | Mathematics/Probability Mathematics/Dynamical Systems Mathematics/Analysis of PDEs |
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| Brownian motion – Stefan problem – mass transport – Skorokhod embedding – Cantelli conjecture |
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| Attached file list to this document: | |||||
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| hal-00666733, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00666733 | |
| oai:hal.archives-ouvertes.fr:hal-00666733 | |
| From: Aline Kurtzmann | |
| Submitted on: Thursday, 9 February 2012 13:51:12 | |
| Updated on: Friday, 16 March 2012 09:02:38 | |
