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2012 An Inverse Problem for a Class of Linear Stochastic Evolution Equations
Yuhuan Zhao
J. Appl. Math. 2012: 1-25 (2012). DOI: 10.1155/2012/921038


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.


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Yuhuan Zhao. "An Inverse Problem for a Class of Linear Stochastic Evolution Equations." J. Appl. Math. 2012 1 - 25, 2012.


Published: 2012
First available in Project Euclid: 2 January 2013

zbMATH: 1260.60127
MathSciNet: MR2979445
Digital Object Identifier: 10.1155/2012/921038

Rights: Copyright © 2012 Hindawi


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