Exact and fast numerical algorithms for the stochastic wave equation

On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense. 1 Statement of the problem and integral representations Consider the stochastic wave equation ∂X ∂t (t, x)− a2 X ∂x (t, x) = g(t, x) + f(t, x) dW (t, x) (1) with random initial conditions, where W is a Gaussian white noise on the plane. We give shortly the precise statement of the problem. The aim of ∗AMS Subject Classification. Primary, 60h15, 68U20.