Analytic-numerical solution of random parabolic models: a mean square fourier transform approach - María-Consuelo Casabán; Juan-Carlos Cortés; Lucas Jódar (Mathematical Modelling and Analysis, 2018)
This paper deals with the construction of mean square analytic-numerical solution of parabolic partial differential problems where both initial condition and coefficients are stochastic processes. By using a random Fourier transform, an infinite integral form of the solution stochastic process is firstly obtained. Afterwards, explicit expressions for the expectation and standard deviation of the solution are obtained. Since these expressions depend upon random improper integrals, which are not computable in an exact manner, random Gauss-Hermite quadrature formulae are introduced throughout an illustrative example.