Large deviations for squares of Bessel and Ornstein-Uhlenbeck processes

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 Cramer–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.