Berry–Esseen inequalities for discretely observed diffusions

Abstract

For stationary ergodic diffusions satisfying nonlinear homogeneous Itô stochastic differential equations, the paper compares the bounds on the rates of convergence to normality (Berry–Esseen type) of two approximate maximum likelihood estimators of the drift parameter based on the Itô and the Fisk–Stratonovich approximations of the continuous likelihood, under some regularity conditions, when the diffusion is observed at equally spaced dense time points over a long time interval. It shows that the Fisk–Stratonovich approximations performs better than the Itô approximations in the sense of having smaller variance.