Abstract
This paper aims to derive large deviations for statistics of the Jacobi process already conjectured by M. Zani in her thesis. To proceed, we write in a simpler 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. This gives a Mehler-type formula whence we recover the desired semi-group density. Once we do, an adaptation of Zani’s result [M. Zani, Large deviations for squared radial Ornstein–Uhlenbeck processes, Stochastic. Process. Appl. 102 (1) (2002) 25–42] to the non-steep case will provide the required large deviations principle.
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