  We study a stochastic version of the dynamical Casimir effect, computing the
particle creation inside a cavity produced by a random motion of one of its
walls. We first present a calculation perturbative in the amplitude of the
motion. We compare the stochastic particle creation with the deterministic
counterpart. Then we go beyond the perturbative evaluation using a stochastic
version of the multiple scale analysis, that takes into account stochastic
parametric resonance. We stress the relevance of the coupling between the
different modes induced by the stochastic motion. In the single-mode
approximation, the equations are formally analogous to those that describe the
stochastic particle creation in a cosmological context, that we rederive using
multiple scale analysis.
