Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Authors: William E. Boyce and Ning Mao Xia
Journal: Quart. Appl. Math. 40 (1983), 419-445
MSC: Primary 34F05; Secondary 34B25, 60H10
DOI: https://doi.org/10.1090/qam/693876
MathSciNet review: 693876
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Abstract: 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.


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DOI: https://doi.org/10.1090/qam/693876
Article copyright: © Copyright 1983 American Mathematical Society


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