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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 1, 1997, pp. 201–216
DOI: 10.4171/ZAA/759

Published online: 1997-03-31

Distribution Approximations for Nonlinear Functionals of Weakly Correlated Random Processes

J. vom Scheidt[1], S. Mehlhose[2] and R. Wunderlich[3]

(1) Technische Universität Chemnitz, Germany
(2) Technische Universität Chemnitz, Germany
(3) Technische Universität Chemnitz, Germany

In this paper nonlinear functionals of weakly correlated processes with correlation length $\epsilon > 0$ are investigated. Expansions of moments and distribution densities of nonlinear functionals with respect to $\epsilon$ up to terms of order $o(\epsilon)$ are considered. For the case of a single nonlinear functional a shorter proof than in [8] 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 [7] not only first order approximations (exact up to terms of order $O(\epsilon)$) but also second order approximations (exact up to terms of order $o(\epsilon)$) are investigated. These approximations are compared with estimations from Monte-Carlo simulation.

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

vom Scheidt J., Mehlhose S., Wunderlich R.: Distribution Approximations for Nonlinear Functionals of Weakly Correlated Random Processes. Z. Anal. Anwend. 16 (1997), 201-216. doi: 10.4171/ZAA/759