  Acoustic emission or scattering problems naturally involve uncertainties
about the sound sources or boundary conditions. This article initiates the
study of time domain boundary elements for such stochastic boundary problems
for the acoustic wave equation. We present a space-time stochastic Galerkin
boundary element method which is applied to sound-hard, sound-soft and
absorbing scatterers. Uncertainties in both the sources and the boundary
conditions are considered using a polynomial chaos expansion. The numerical
experiments illustrate the performance and convergence of the proposed method
in model problems and present an application to a problem from traffic noise.
