Estimation Problems for Coefficients of Stochastic Partial Differential Equations. Part I
This paper considers the problem of estimating functional parameters $a_k(t,x)$, $f(t,x)$ by observing a solution $u_\ve(t,x)$ of a stochastic partial differential equation $$ du_\ve(t)=\sum_{|k|\le 2p} a_kD_x^ku_\ve+f\,dt+\ve\,dw(t), $$ where $w(t)$ is a Wiener process. The asymptotic statement of...
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Veröffentlicht in: | Theory of probability and its applications 1999-01, Vol.43 (3), p.370-387 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | This paper considers the problem of estimating functional parameters $a_k(t,x)$, $f(t,x)$ by observing a solution $u_\ve(t,x)$ of a stochastic partial differential equation $$ du_\ve(t)=\sum_{|k|\le 2p} a_kD_x^ku_\ve+f\,dt+\ve\,dw(t), $$ where $w(t)$ is a Wiener process. The asymptotic statement of the problem is considered when the noise level $\ve\to 0$. In the first part of the work we determine what is considered the statistics of the problem and investigate the problem of estimating f. |
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ISSN: | 0040-585X 1095-7219 |
DOI: | 10.1137/S0040585X97976982 |