Large deviations for statistics of the Jacobi process. (English) Zbl 1158.60008
Summary: 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 M. Zani [Stochastic Processes Appl. 102, No. 1, 25–42 (2002; Zbl 1075.62535)] to the non-steep case will provide the required large deviations principle.
MSC:
| 60F10 | Large deviations |
| 60G05 | Foundations of stochastic processes |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 62F12 | Asymptotic properties of parametric estimators |
Citations:
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