Access the full text.
Sign up today, get DeepDyve free for 14 days.
S. Gutman (1990)
Identification of discontinuous parameters in flow equationsSiam Journal on Control and Optimization, 28
L. Gerencsér (1989)
On a class of mixing processesStochastics and Stochastics Reports, 26
S. Aihara, Y. Sunahara (1987)
Identification of an infinite dimensional parameter for stochastic diffusion equation26th IEEE Conference on Decision and Control, 26
D. Nualart, É. Pardoux (1988)
Stochastic calculus with anticipating integrandsProbability Theory and Related Fields, 78
W. Fleming, É. Pardoux (1982)
Optimal Control for Partially Observed DiffusionsSiam Journal on Control and Optimization, 20
S. Aihara (1992)
Regularized maximum likelihood estimate for an infinite-dimensional parameter in stochastic parabolic systemsSiam Journal on Control and Optimization, 30
E. Giusti (1977)
Minimal surfaces and functions of bounded variation
N. Ahmed, K. Teo (1981)
Optimal control of distributed parameter systems
David Levanony, A. Shwartz, O. Zeitouni (1994)
Recursive identification in continuous-time stochastic processesStochastic Processes and their Applications, 49
David Levanony, A. Schwartz, Ofer Zettount (1993)
Uniform Decay and Equicontinuity for Normalized, Parameter Dependent, ITO IntegralsStochastics and Stochastics Reports, 43
S. Aihara, A. Bagchi (1991)
Parameter identification for hyperbolic stochastic systemsJournal of Mathematical Analysis and Applications, 160
V. Benes, I. Karatzas (1983)
On the Relation of Zakai’s and Mortensen’s EquationsSiam Journal on Control and Optimization, 21
H. Banks, K. Kunisch (1989)
Estimation Techniques for Distributed Parameter Systems
A. Balakrishnan (1976)
Applied Functional Analysis
J. Lions (1971)
Optimal Control of Systems Governed by Partial Differential Equations
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.
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2006
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.