  In this paper, we consider a linear model with jumps driven by a Brownian
motion and a compensated Poisson process, whose drift and diffusion
coefficients as well as its intensity are unknown parameters. Supposing that
the process is observed discretely at high frequency we derive the local
asymptotic normality (LAN) property. In order to obtain this result, Malliavin
calculus and Girsanov's theorem are applied in order to write the
log-likelihood ratio in terms of sums of conditional expectations, for which a
central limit theorem for triangular arrays can be applied.
