  By combining the Malliavin calculus with Fourier techniques, we develop a
high-order asymptotic expansion theory for a sequence of vector-valued random
variables. Our asymptotic expansion formulas give the development of the
characteristic functional and of the local density of the random vectors up to
an arbitrary order. We analyzed in details an example related to the wave
equation with space-time white noise which also provides interesting facts on
the correlation structure of the solution to this equation.
