Deviation properties for linear self-attracting diffusion process and applications

Abstract

In this paper, we study explicitly the deviation properties, including the deviation inequalities and Cramér-type moderate deviations, for some quadratic functionals of linear self-attracting diffusion process. As applications, Cramér-type moderate deviations for the log-likelihood ratio process and drift parameter estimator are obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener–Itô integrals, as well as the asymptotic analysis techniques.