In this paper nonlinear functionals of weakly correlated processes with correlation length are investigated. Expansions of moments and distribution densities of nonlinear functionals with respect to up to terms of order are considered. For the case of a single nonlinear functional a shorter proof than in  is given. The results are applied to cigenvalues 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 cigenvalues can be found. In addition to  not only first order approximations (exact up to terms of order ) but also second order approximations (exact up to terms of order ) are investigated. These approximations are compared with estimations from Monte-Carlo simulation.
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J. vom Scheidt, S. Mehlhose, R. Wunderlich, Distribution Approximations for Nonlinear Functionals of Weakly Correlated Random Processes. Z. Anal. Anwend. 16 (1997), no. 1, pp. 201–216DOI 10.4171/ZAA/759