I. A. Ibragimov, R. Z. Khas'minskii, “Estimation problems for coefficients of stochastic partial differential equations. Part II”, Teor. Veroyatnost. i Primenen., 44:3 (1999), 526–554; Theory Probab. Appl., 44:3 (2000), 469

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Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 3, Pages 526–554
DOI: https://doi.org/10.4213/tvp802 (Mi tvp802)

This article is cited in 11 scientific papers (total in 12 papers)

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

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, USA

Full-text PDF (1273 kB) Citations (12)

DOI: https://doi.org/10.4213/tvp802

Abstract: As in Part I (see [I. A. Ibragimov and R. Z. Khas'minskii, Theory Probab. Appl., 43 (1999), pp. 370–387]), we consider the problem of estimation of functional parameters

a_{k} (t, x), θ (t, x)

$a_k(t,x),\theta(t,x)$ by observing a solution

u_{ε} (t, x)

$u_\varepsilon(t,x)$ of a stochastic partial differential equation

$du_\varepsilon(t)=\sum_{|k|\le 2p}a_kD_x^ku_\varepsilon+\theta\,dt+\varepsilon\,dw(t),$
where

$w(t)$ is a Wiener process. We investigate problems of the existence of consistent estimates for

$\theta$ and their rate of convergence to

$\theta$ dependent on properties of the functional class

$\Theta$ , which a priori contains

$\theta$ .

Keywords: inverse problems, stochastic differential equations, statistical estimation, nonparametric estimating problems.

Received: 09.12.1997

English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 3, Pages 469–494
DOI: https://doi.org/10.1137/S0040585X97977720

Bibliographic databases:

Language: Russian

Citation: I. A. Ibragimov, R. Z. Khas'minskii, “Estimation problems for coefficients of stochastic partial differential equations. Part II”, Teor. Veroyatnost. i Primenen., 44:3 (1999), 526–554; Theory Probab. Appl., 44:3 (2000), 469–494

Citation in format AMSBIB

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\pages 526--554

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\jour Theory Probab. Appl.

\yr 2000

\vol 44

\issue 3

\pages 469--494

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Linking options:

https://www.mathnet.ru/eng/tvp802

https://doi.org/10.4213/tvp802

https://www.mathnet.ru/eng/tvp/v44/i3/p526

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

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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
A. A. Zaikin, “Asymptotic expansion of posterior distribution of parameter centered by a $\sqrt n$ -consistent estimate”, J. Math. Sci. (N. Y.), 229:6 (2018), 678–697
Liu Sh., Zhang Y., “Stability of Stochastic 2-D Systems”, Appl. Math. Comput., 219:1 (2012), 197–212
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”, Publ. Mat., 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
Lototsky S.V., “Optimal filtering of stochastic parabolic equations”, Recent developments in stochastic analysis and related topics, World Sci. Publ., Hackensack, NJ, 2004, 330–353
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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