Weak convergence of approximate solutions of stochastic equations with applications to random differential and integral equations

Authors: Heinz W. Engl and Werner Römisch

Abstract: In this paper, we considerably extend our earlier result about convergence in distribution of approximate solutions of random operator equations, where the stochastic inputs and the underlying deterministic equation are simultaneously appoximated. As a by-product, we obtain convergence results for approximate solutions of equations between spaces of probability measures. We apply our results to random Fredholm integral equations of the second kind and to a random nonlinear elliptic boundary value problem.