Random walk methods and wave diffraction

This paper develops an approach to problems of wave diffraction that combines the physical clarity of the ray method with the versatility of direct numerical methods. First it addresses scalar problems with general linear first-order boundary conditions, and then it considers problems formulated in adjacent domains with imposed interface conditions. We start by following closely the scheme of the ray method, but instead of looking for approximate expressions for the amplitudes of the Liouville decomposition we obtain their exact representations as the mathematical expectations of some functionals on the space of Brownian trajectories. The obtained solutions provide direct improvements of the ray method approximations to the exact solutions, and they are shown to admit efficient numerical evaluations