Distribution approximations for nonlinear functionals of weakly correlated random processes
type: Item
instance of: scholarly article
title: Distribution approximations for nonlinear functionals of weakly correlated random processes
zbMATH Open document ID: 0883.60060
DOI: 10.4171/ZAA/759
author: J. vom Scheidt
author: S. Mehlhose
author: R. Wunderlich
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1998-03-04T00:00:00Z
review text: Summary: Nonlinear functionals of weakly correlated processes with correlation length \(\varepsilon> 0\) are investigated. Expansions of moments and distribution densities of nonlinear functionals with respect to \(\varepsilon\) up to terms of order \(o(\varepsilon)\) are considered. For the case of a single nonlinear functional a shorter proof than in [the first author, ``Stochastic equations of mathematical physics'' (1990; Zbl 0715.60061)] 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 \(\varepsilon\) approximations of the density functions of the matrix eigenvalues can be found. In addition to [the first author and \textit{W. Purkert}, ``Random eigenvalue problems'' (1984; Zbl 0585.60062)] not only first-order approximations (exact up to terms of order \(O(\varepsilon)\)) but also second-order approximations (exact up to terms of order \(o(\varepsilon)\)) are investigated. These approximations are compared with estimations from Monte-Carlo simulation.
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 65L15
zbMATH DE Number: 1011110
zbMATH Keywords: random functions
zbMATH Keywords: weakly correlated processes
zbMATH Keywords: random matrix eigenvalue problems
MaRDI profile type: Publication
cites work: The approach to normality of the solutions of random boundary and eigenvalue problems with weakly correlated coefficients
cites work: Q4320719
cites work: Q5588093
cites work: Q3709558
cites work: Q4692354
full work available at URL: https://doi.org/10.4171/zaa/759
OpenAlex ID: W2011102796
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description: scientific article; zbMATH DE number 1011110