Large Deviations and Berry–Esseen Inequalities for Estimators in Nonlinear Nonhomogeneous Diffusions

Abstract

Bounds on the large deviations probability of the maximum likelihood estimator and regular Bayes estimators, and Berry–Esseen type bound for the suitably normalized maximum likelihood estimator of a parameter appearing nonlinearly in the nonhomogeneous drift coefficient of Itˆo stochastic differential equation are obtained under some regularity conditions. Berry–Esseen results are illustrated for nonhomogeneous Ornstein–Uhlebeck process.