Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

We first consider a multidimensional diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a Lévy process without Gaussian component, whose drift coefficient depends on a multidimensional unknown parameter. We prove the local asymptotic normality (LAN) property from high-frequency discrete observations with increasing observation window by assuming some hypotheses on the coefficients of the equation, the ergodicity of the solution and the integrability of the Lévy measure. Second, we prove the local asymptotic mixed normality (LAMN) property for the drift parameter of a multidimensional inhomogeneous diffusion under some appropriate assumptions on the coefficients. To obtain these results, we use the Malliavin calculus techniques and the Girsanov change of measures. Joint work with Hoang Long Ngo.