Diffraction of a plane wave by a sector with Dirichlet or Neumann boundary conditions

The problems of diffraction by a screen occupying an infinite sector with Dirichlet or Neumann boundary conditions are addressed by the random walk method. The solution is represented as a superposition of the wave field completely determined by an elementary ray analysis and of the field formed by the waves diffracted by the tip of the screen. The diffracted field is explicitly represented as a mathematical expectation of a specified functional on trajectories of a random motion whose behavior is determined by the configuration of the problem and by the boundary conditions. The numerical results confirm the efficiency of the random walk approach to the analysis of diffraction by wedge-shaped screens of different angles.