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Teor. Veroyatnost. i Primenen., 2000, Volume 45, Issue 2, Pages 209–235 (Mi tvp460)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.4213/tvp460

Full text: PDF file (1137 kB)

English version:
Theory of Probability and its Applications, 2001, 45:2, 210–232

Bibliographic databases:

Received: 09.12.1997

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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\paper Estimation problems for coefficients of stochastic partial differential equations. Part~III
\jour Teor. Veroyatnost. i Primenen.
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\issue 2
\pages 209--235
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\crossref{https://doi.org/10.4213/tvp460}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1967754}
\zmath{https://zbmath.org/?q=an:0983.62053}
\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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Ibragimov, “One Estimation Problem for Quasilinear Stochastic Partial Differential Equations”, Problems Inform. Transmission, 39:1 (2003), 51–77  mathnet  crossref  mathscinet  zmath
    2. Lototsky S.V., “Statistical Inference for Stochastic Parabolic Equations: a Spectral Approach”, Publicacions Matematiques, 53:1 (2009), 3–45  crossref  mathscinet  zmath  isi  scopus
    3. Liu W., Lototsky S.V., “Parameter estimation in hyperbolic multichannel models”, Asymptot Anal, 68:4 (2010), 223–248  crossref  mathscinet  zmath  isi  elib  scopus
    4. Lototsky S. Rozovsky B., “Stochastic Partial Differential Equations”, Stochastic Partial Differential Equations, Universitext, Springer, 2017, 1–508  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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