Journal of Applied Mathematics

An Inverse Problem for a Class of Linear Stochastic Evolution Equations

Yuhuan Zhao

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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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 921038, 25 pages.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153507

Digital Object Identifier
doi:10.1155/2012/921038

Mathematical Reviews number (MathSciNet)
MR2979445

Zentralblatt MATH identifier
1260.60127

Citation

Zhao, Yuhuan. An Inverse Problem for a Class of Linear Stochastic Evolution Equations. J. Appl. Math. 2012 (2012), Article ID 921038, 25 pages. doi:10.1155/2012/921038. https://projecteuclid.org/euclid.jam/1357153507


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