  Given a sample from a discretely observed multidimensional compound Poisson
process, we study the problem of nonparametric estimation of its jump size
density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian
approach to the problem and determine posterior contraction rates in this
context, which, under some assumptions, we argue to be optimal posterior
contraction rates. In particular, our results imply the existence of Bayesian
point estimates that converge to the true parameter pair $(r_0,\lambda_0)$ at
these rates. To the best of our knowledge, construction of nonparametric
density estimators for inference in the class of discretely observed
multidimensional L\'{e}vy processes, and the study of their rates of
convergence is a new contribution to the literature.
