Large deviations for squares of Bessel and Ornstein-Uhlenbeck processes |
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| Authors: | Email author" target="_blank">C?Donati-MartinEmail author A?Rouault M?Yor M?Zani |
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| Institution: | (1) Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, Site Chevaleret, 13 rue Clisson, F-75013 Paris, France;(2) LAMA, Bâtiment Fermat, Université de Versailles, F-78035 Versailles, France;(3) Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, Site Chevaleret, 13 rue Clisson, F-75013 Paris, France;(4) Laboratoire d Analyse et de Mathématiques Appliquées, CNRS UMR 8050, Université Paris 12-Val de Marne, 61, avenue du Général de Gaulle, F-94010 Créteil, France |
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| Abstract: | Let (Xt( ),t 0) be the BESQ process starting at x. We are interested in large deviations as
for the family {–1Xt(),t T}, – or, more generally, for the family of squared radial OU process. The main properties of this family allow us to develop three different approaches: an exponential martingale method, a Cramér–type theorem, thanks to a remarkable additivity property, and a Wentzell–Freidlin method, with the help of McKean results on the controlled equation. We also derive large deviations for Bessel bridges.Mathematics Subject Classification (2000): 60F10, 60J60 |
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| Keywords: | Bessel processes Ornstein-Uhlenbeck processes Additivity property Large deviation principle |
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