The approach to normality of the solutions of random boundary and eigenvalue problems with weakly correlated coefficients

A general class of linear self-adjoint random boundary value problems with weakly correlated coefficients is considered. The earlier result that the distribution function of the solution approaches the normal as the correlation length $\epsilon$ tends to zero is generalized somewhat. Correction terms are derived that yield estimates for the distribution function when $\epsilon$ is small but nonzero. The results are also applied to the eigenvalues and eigenfunctions of a corresponding class of random eigenvalue problems. The discussion is given in terms of second-order equations, but extensions to higher-order problems are readily apparent.