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Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 4, Pages 214–221 (Mi timm1015)  

This article is cited in 1 scientific paper (total in 1 paper)

Problem of reconstructing a disturbance in a linear stochastic equation: the case of incomplete information

V. L. Rozenberg

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: The problem of reconstructing an unknown deterministic disturbance characterizing the level of random noise in a linear stochastic second-order equation is investigated based on the approach of dynamic inversion theory. The reconstruction is performed with the use of discrete information on a number of realizations of one coordinate of the stochastic process. The problem under consideration is reduced to an inverse problem for a system of ordinary differential equations describing the covariance matrix of the original process. A finite-step solving algorithm based on the method of auxiliary controlled models is suggested. Its convergence rate estimate with respect to the number of measured realizations is obtained.

Keywords: reconstruction of disturbance, stochastic differential equation, incomplete input information.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 287, suppl. 1, 167–174

Bibliographic databases:

UDC: 517.977
Received: 31.05.2013

Citation: V. L. Rozenberg, “Problem of reconstructing a disturbance in a linear stochastic equation: the case of incomplete information”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 214–221; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 167–174

Citation in format AMSBIB
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\by V.~L.~Rozenberg
\paper Problem of reconstructing a disturbance in a linear stochastic equation: the case of incomplete information
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 4
\pages 214--221
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\elib{http://elibrary.ru/item.asp?id=20640516}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 287
\issue , suppl. 1
\pages 167--174
\crossref{https://doi.org/10.1134/S0081543814090168}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84912032137}


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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. V. L. Rozenberg, “Reconstruction of external actions under incomplete information in a linear stochastic equation”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 196–205  mathnet  crossref  crossref  mathscinet  isi  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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