Identification of a Discontinuous Parameter in Stochastic Parabolic Systems |
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Authors: | S I Aihara |
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Institution: | (1) Department of Management and Systems Science, The Science University of Tokyo, Suwa College, 5000-2 Toyohira, Chino 391-02, Nagano, Japan , JP |
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Abstract: | The purpose of this paper is to study the identification problem for a spatially varying discontinuous parameter in stochastic
diffusion equations. The consistency property of the maximum likelihood estimate (M.L.E.) and a generating algorithm for M.L.E.
have been explored under the condition that the unknown parameter is in a sufficiently regular space with respect to spatial
variables. In order to prove the consistency property of the M.L.E. for a discontinuous diffusion coefficient, we use the
method of sieves, i.e., first the admissible class of unknown parameters is projected into a finite-dimensional space and
next the convergence of the derived finite-dimensional M.L.E. to the infinite-dimensional M.L.E. is justified under some conditions.
An iterative algorithm for generating the M.L.E. is also proposed with two numerical examples.
Accepted 2 April 1996 |
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Keywords: | , Maximum likelihood estimate, Consistent estimate, The method of sieves, Stochastic parabolic equations, AMS Classification,,,,,,Primary 93C20, 93E12, Secondary 60H15, |
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