  We prove sufficient conditions, ensuring that a sequence of multiple
Wiener-It\^{o} integrals (with respect to a general Gaussian process) converges
stably to a mixture of normal distributions. Our key tool is an asymptotic
decomposition of contraction kernels, realized by means of increasing families
of projection operators. We also use an infinite-dimensional Clark-Ocone
formula, as well as a version of the correspondence between "abstract" and
"concrete" filtered Wiener spaces, in a spirit similar to \"{U}st\"{u}nel and
Zakai (1997).
