A random Laplace transform method for solving random mixed parabolic differential problems

This paper deals with the explicit solution of random mixed parabolic equations in unbounded domains by using the random Laplace transform to second order stochastic processes. The mean square random Laplace operational calculus is stated and its application to the random parabolic equation together with previous results of the underlying random ordinary differential equations allow us to obtain an explicit solution of the problem. A numerical example, which includes simulations, illustrates the developed method.