  We consider a real-valued diffusion process with a linear jump term driven by
a Poisson point process and we assume that the jump amplitudes have a centered
density with finite moments. We show upper and lower estimates for the density
of the solution in the case that the jump amplitudes follow a Gaussian or
Laplacian law. The proof of the lower bound uses a general expression for the
density of the solution in terms of the convolution of the density of the
continuous part and the jump amplitude density. The upper bound uses an upper
tail estimate in terms of the jump amplitude distribution and techniques of the
Malliavin calculus in order to bound the density by the tails of the solution.
We also extend the lower bounds to the multidimensional case.
