Journées de Probabilités 2007

Marguerite Zani

Large deviations for statistics of Jacobi processes

(In collaboration with N. Demni)

We derive large deviations for statistics of Jacobi processes. To proceed, we write in a more simple way the Jacobi semi-group density. Being given by a bilinear sum involving Jacobi polynomials, it differs from Hermite and Laguerre cases by the quadratic form of its eigenvalues. Our attempt relies on subordinating the process using a suitable random time-change. We can recover the desired expression by inverting some Laplace tranforms. Then we conclude with a large deviations principle in a non steep-case.