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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 3, Pages 377–386 (Mi zvmmf10363)  

This article is cited in 2 scientific papers (total in 2 papers)

Reconstruction of random-disturbance amplitude in linear stochastic equations from measurements of some of the coordinates

V. L. Rozenberg

Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

Abstract: The problem of reconstructing the unknown amplitude of a random disturbance in a linear stochastic differential equation is studied in a fairly general formulation by applying dynamic inversion theory. The amplitude is reconstructed using discrete information on several realizations of some of the coordinates of the stochastic process. The problem is reduced to an inverse one for a system of ordinary differential equations satisfied by the elements of the covariance matrix of the original process. Constructive solvability conditions in the form of relations on the parameters of the system are discussed. A finite-step software implementable solving algorithm based on the method of auxiliary controlled models is tested using a numerical example. The accuracy of the algorithm is estimated with respect to the number of measured realizations.

Key words: dynamic reconstruction, stochastic differential equation, incomplete input data, finite-step algorithm, error estimation.

Funding Agency Grant Number
Russian Science Foundation 14-11-00539


DOI: https://doi.org/10.7868/S0044466916030169

Full text: PDF file (306 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:3, 367–375

Bibliographic databases:

UDC: 519.626
Received: 22.10.2014
Revised: 26.10.2015

Citation: V. L. Rozenberg, “Reconstruction of random-disturbance amplitude in linear stochastic equations from measurements of some of the coordinates”, Zh. Vychisl. Mat. Mat. Fiz., 56:3 (2016), 377–386; Comput. Math. Math. Phys., 56:3 (2016), 367–375

Citation in format AMSBIB
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\paper Reconstruction of random-disturbance amplitude in linear stochastic equations from measurements of some of the coordinates
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 3
\pages 377--386
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\crossref{https://doi.org/10.7868/S0044466916030169}
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\transl
\jour Comput. Math. Math. Phys.
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\vol 56
\issue 3
\pages 367--375
\crossref{https://doi.org/10.1134/S0965542516030143}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. L. Rozenberg, “Dynamic reconstruction of disturbances in a quasilinear stochastic differential equation”, Comput. Math. Math. Phys., 58:7 (2018), 1071–1080  mathnet  crossref  crossref  isi  elib
    2. Rozenberg V.L., “Dynamical Input Reconstruction Problem For a Quasi-Linear Stochastic System”, IFAC PAPERSONLINE, 51:32 (2018), 727–732  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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