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Preprint, Working Paper, ... |
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| Title: |
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A counter-example to the Cantelli conjecture |
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| Author(s): |
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Victor Kleptsyn ( ) 1, Aline Kurtzmann () 2 |
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| Laboratory: |
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| Research team: |
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Géométrie analytique
Probabilités et statistiques |
| Abstract: |
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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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| Fulltext language: |
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English |
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| Production date: |
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2012-02-03 |
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| Keyword(s): |
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Brownian motion – Stefan problem – mass transport – Skorokhod embedding – Cantelli conjecture |
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| Comment: |
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37 pages |
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