In this paper, we consider a multidimensional ergodic diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a compound Poisson process, whose drift coefficient depends on an unknown parameter. Considering the process discretely observed at high frequency, we derive the local asymptotic normality (LAN) property.

The first author was supported by KAKENHI grant 24340022 and a JST-CREST project Mathematical structure of complex financial products and infinite dimensional analysis. Second author acknowledges support from the European Union programme FP7-PEOPLE-2012-CIG under grant agreement 333938. Third author acknowledges support from JST-CREST project and the program Vietnam Overseas Scholarship Program (Project 322) and wishes to thank Université Paris 13 for the hospitality where a part of this work was done.