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Teoriya Veroyatnostei i ee Primeneniya, 2000, Volume 45, Issue 2, Pages 209–235
DOI: https://doi.org/10.4213/tvp460 (Mi tvp460) 		 
This article is cited in 8 scientific papers (total in 9 papers)

Estimation problems for coefficients of stochastic partial differential equations. Part III

I. A. Ibragimova, R. Z. Khas'minskiib

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Wayne State University, Detroit, USA
Full-text PDF (1137 kB) Citations (9)
DOI: https://doi.org/10.4213/tvp460
Abstract: This paper is concerned with the problem of estimating a functional parameter $a_0(t,x)$ upon observation of a solution $u_\varepsilon(t,x)$ of the stochastic partial differential equation
$$ du_\varepsilon(t)=\sum_{|k|\le 2p}a_kD_x^ku_\varepsilon\,dt+f\,dt+\varepsilon\,dw(t)=0. $$
Asymptotically minimax estimates for $a_0$ and asymptotically effective estimates for $\Phi(a_0)$ are found under the assumption that $a_0$ is independent of $t$.
Keywords: inverse problems, stochastic partial differential equations, statistical estimation, nonparametric problems of estimating.
Received: 09.12.1997
English version:
Theory of Probability and its Applications, 2001, Volume 45, Issue 2, Pages 210–232
DOI: https://doi.org/10.1137/S0040585X9797818X
Bibliographic databases:
Language: Russian
Citation: I. A. Ibragimov, R. Z. Khas'minskii, “Estimation problems for coefficients of stochastic partial differential equations. Part III”, Teor. Veroyatnost. i Primenen., 45:2 (2000), 209–235; Theory Probab. Appl., 45:2 (2001), 210–232
Citation in format AMSBIB
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\transl
\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 2
\pages 210--232
\crossref{https://doi.org/10.1137/S0040585X9797818X}
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  • https://www.mathnet.ru/eng/tvp/v45/i2/p209
    Cycle of papers
    This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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