  Using Stein's method and the Malliavin calculus of variations, we derive
explicit estimates for the Gamma approximation of functionals of a Poisson
measure. In particular, conditions are presented under which the distribution
of a sequence of multiple Wiener-Ito stochastic integrals with respect to a
compensated Poisson measure converges to a Gamma distribution. As an
illustration, we present a quantitative version and a non-central extension of
a classical theorem by de Jong in the case of degenerate U-statistics of order
two. Several multidimensional extensions, in particular allowing for mixed or
hybrid limit theorems, are also provided.
