  We combine Malliavin calculus with Stein's method, in order to derive
explicit bounds in the Gaussian and Gamma approximations of random variables in
a fixed Wiener chaos of a general Gaussian process. We also prove results
concerning random variables admitting a possibly infinite Wiener chaotic
decomposition. Our approach generalizes, refines and unifies the central and
non-central limit theorems for multiple Wiener-It\^o integrals recently proved
(in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre,
Peccati and Tudor. We apply our techniques to prove Berry-Ess\'een bounds in
the Breuer-Major CLT for subordinated functionals of fractional Brownian
motion. By using the well-known Mehler's formula for Ornstein-Uhlenbeck
semigroups, we also recover a technical result recently proved by Chatterjee,
concerning the Gaussian approximation of functionals of finite-dimensional
Gaussian vectors.
