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International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 497-516
http://dx.doi.org/10.1155/S0161171286000625

Linear random boundary value problems containing weakly correlated forcing functions

East China Institute of Chemical Technology, Shanghai, China

Received 20 March 1984

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper concerns linear random boundary value problems that contain random variables In the boundary conditions and weakly correlated processes in the differential equations. When the correlation length ϵ is small the structure of the solution is pointed out, and the formulas for the density function of the solutions are derived. The discussion is given in terms of second order equations, but extensions to higher order problems are readily apparent.