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Journal of Applied Mathematics
Volume 2012, Article ID 921038, 25 pages
http://dx.doi.org/10.1155/2012/921038
Research Article

An Inverse Problem for a Class of Linear Stochastic Evolution Equations

College of Science, Civil Aviation University of China, Tianjin 300300, China

Received 8 May 2012; Revised 7 August 2012; Accepted 9 August 2012

Academic Editor: Chong Lin

Copyright © 2012 Yuhuan Zhao. 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

An inverse problem for a linear stochastic evolution equation is researched. The stochastic evolution equation contains a parameter with values in a Hilbert space. The solution of the evolution equation depends continuously on the parameter and is Fréchet differentiable with respect to the parameter. An optimization method is provided to estimate the parameter. A sufficient condition to ensure the existence of an optimal parameter is presented, and a necessary condition that the optimal parameter, if it exists, should satisfy is also presented. Finally, two examples are given to show the applications of the above results.