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| HAL : hal-00727129, version 2 |
| arXiv : 1209.0189 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (02-09-2012) | v2 (17-09-2012) |
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| On the Csáki-Vincze transformation |
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| Hatem Hajri 1 |
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| (02/09/2012) |
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| Cs aki and Vincze have de fined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and assymptotic properties of T . We prove that T is exact : \cap_{k\geq 1} \sigma(T^k(S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k. We then show that, in a suitable scaling limit, all iterations of T "converge" to the corresponding iterations of the continous L evy transform of Brownian motion. Some consequences are also derived from these two results. |
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| 1 : | Université du Luxembourg |
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Université de Luxembourg |
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| Domaine | : | Mathématiques/Probabilités |
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| Lévy transformation – Csaki-Vincze transformation – Brownian motion. |
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| hal-00727129, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00727129 | |
| oai:hal.archives-ouvertes.fr:hal-00727129 | |
| Contributeur : Hatem Hajri | |
| Soumis le : Samedi 15 Septembre 2012, 16:15:43 | |
| Dernière modification le : Mardi 23 Avril 2013, 13:31:33 | |
