Computation of moment functions for parabolic PDEs with random parameters

This paper deals with different approaches for the computation of stochastic characteristics (such as mean, variance, correlation function, …) of the solution to parabolic PDEs with random parameters, in particular with a random Neumann boundary conditions and a random initial condition. Thereby Finite-Element discretisation of the spatial variables is used for the construction of pathwise solutions. The random influences are assumed to be ε -correlated (cp. 4]) that means the correlation functions vanish if the difference of the arguments exceeds a given correlation length ε . So an asymptotic expansion of higher order with respect to the correlation length for the correlation function of the approximative solution is given. A second possibility is the so called explicit calculation. Examples which compare the different methods can be found in 2]. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)