Abstract.
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),t≤T}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.
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Mathematics Subject Classification (2000): 60F10, 60J60
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Donati-Martin, C., Rouault, A., Yor, M. et al. Large deviations for squares of Bessel and Ornstein-Uhlenbeck processes. Probab. Theory Relat. Fields 129, 261–289 (2004). https://doi.org/10.1007/s00440-004-0338-y
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DOI: https://doi.org/10.1007/s00440-004-0338-y