Probability Theory and Related Fields

, Volume 129, Issue 2, pp 261–289 | Cite as

Large deviations for squares of Bessel and Ornstein-Uhlenbeck processes

  • C. Donati-Martin
  • A. Rouault
  • M. Yor
  • M. Zani


Let (X t (δ) ,t≥0) be the BESQδ process starting at δx. We are interested in large deviations as \({{\delta \rightarrow \infty}}\) for the family {δ−1 X t (δ) ,tT}δ, – or, more generally, for the family of squared radial OUδ 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.


Bessel processes Ornstein-Uhlenbeck processes Additivity property Large deviation principle 


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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles AléatoiresParisFrance
  2. 2.LAMA, Bâtiment FermatUniversité de VersaillesVersaillesFrance
  3. 3.Laboratoire de Probabilités et Modèles AléatoiresParisFrance
  4. 4.Laboratoire d’Analyse et de Mathématiques AppliquéesCréteilFrance

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