Journal for Analysis and its Appications 16(1997)1, 201-216

Abstract

In this paper nonlinear functionals of weakly correlated processes with correlation length $\e > 0$ are investigated.Expansions of moments and distribution densities of nonlinear functionals with respect to $\e$ up to terms of order $o(\e)$ are considered. For the case of a single nonlinear functional a shorter proof than in [8] is given. The results are applied to eigenvalues of random matrices which are obtained by application of the Ritz method to random differential operators. Using the expansion formulas as to $\e$ approximations of the density functions of the matrix-eigenvalues can be found. In addition to [7] not only first order approximations (exact up to terms of order $O(\e)$) but also second order approximations (exact up to terms of order $o(\e)$) are investigated. These approximations are compared with estimations from Monte-Carlo simulation.

Keywords : Random functions, weakly correlated processes, random matrix eigenvalue problems