Large deviations for squares of Bessel and Ornstein-Uhlenbeck processes

Let (Xt(δ),t≥0) be the BESQδ process starting at δx. We are interested in large deviations as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${{\delta \rightarrow \infty}}$\end{document} for the family {δ−1Xt(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.