Large deviations for the squared radial Ornstein-Uhlenbeck process

TL;DR

This paper derives large deviation principles for the joint estimation of parameters in the squared radial Ornstein-Uhlenbeck process, focusing on the case where the dimensional parameter exceeds 2 and the drift is negative.

Contribution

It provides the first large deviation results for simultaneous estimation of both dimensional and drift coefficients in this process.

Findings

Large deviation principles established for estimators

Focus on the case with a>2 and b<0

Simultaneous estimation analyzed

Abstract

We establish large deviation principles for the couple of the maximum likelihood estimators of dimensional and drift coefficients in the generalised squared radial Ornstein-Uhlenbeck process. We focus our attention to the most tractable situation where the dimensional parameter $a>2$ and the drift parameter $b<0$. In contrast to the previous literature, we state large deviation principles when both dimensional and drift coefficient are estimated simultaneously.