LAMN property for jump diffusion processes with discrete observations on a fixed time interval

Abstract

We consider a one-dimensional stochastic differential equation with jumps driven by a Brownian motion and an independent Lévy process with finite Lévy measure, whose drift and diffusion coefficients depend on an unknown parameter. Under smoothness and non-degeneracy assumptions on the drift and diffusion coefficients and integrability assumption of jump size distribution, we prove the Local Asymptotic Mixed Normality property when the solution process is observed discretely at high frequency on a fixed time interval. The proof is essentially based on Malliavin calculus techniques and an analysis of the jump structure of the Lévy process.