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

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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. Ibragimov^a, R. Z. Khas'minskii^b

^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)

$a_0(t,x)$ upon observation of a solution

u_{ε} (t, x)

$u_\varepsilon(t,x)$ 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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\pages 209--235

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\jour Theory Probab. Appl.

\yr 2001

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Linking options:

https://www.mathnet.ru/eng/tvp460

https://doi.org/10.4213/tvp460

https://www.mathnet.ru/eng/tvp/v45/i2/p209

Cycle of papers

Estimation problems for coefficients of stochastic partial differential equations. Part II
I. A. Ibragimov, R. Z. Khas'minskii
Teor. Veroyatnost. i Primenen., 1999, 44:3, 526–554
Estimation problems for coefficients of stochastic partial differential equations. Part III
I. A. Ibragimov, R. Z. Khas'minskii
Teor. Veroyatnost. i Primenen., 2000, 45:2, 209–235

This publication is cited in the following 9 articles:

A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583
Sascha Gaudlitz, Markus Reiß, “Estimation for the reaction term in semi-linear SPDEs under small diffusivity”, Bernoulli, 29:4 (2023)
Igor Cialenco, “Statistical inference for SPDEs: an overview”, Stat Inference Stoch Process, 21:2 (2018), 309
Lototsky S. Rozovsky B., “Stochastic Partial Differential Equations”, Stochastic Partial Differential Equations, Universitext, Springer, 2017, 1–508
Yuhuan Zhao, Chong Lin, “An Inverse Problem for a Class of Linear Stochastic Evolution Equations”, Journal of Applied Mathematics, 2012:1 (2012)
Liu W., Lototsky S.V., “Parameter estimation in hyperbolic multichannel models”, Asymptot Anal, 68:4 (2010), 223–248
Lototsky S.V., “Statistical Inference for Stochastic Parabolic Equations: a Spectral Approach”, Publicacions Matematiques, 53:1 (2009), 3–45
Igor Cialenco, Sergey V. Lototsky, “Parameter estimation in diagonalizable bilinear stochastic parabolic equations”, Stat Inference Stoch Process, 12:3 (2009), 203
I. A. Ibragimov, “An Estimation Problem for Quasilinear Stochastic Partial Differential Equations”, Problems Inform. Transmission, 39:1 (2003), 51–77

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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