Large deviations for statistics of the Jacobi process

N. Demni and M. Zani

Stochastic Processes and their Applications, 2009, vol. 119, issue 2, 518-533

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.

Keywords: Jacobi; process; Subordinated; Jacobi; process; Large; deviations; Maximum; likelihood (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (8)

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