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

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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 with respect to the number of measured realizations is estimated.

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Authors and Affiliations

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

    V. L. Rozenberg

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  1. V. L. Rozenberg
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Correspondence to V. L. Rozenberg.

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Original Russian Text © V.L. Rozenberg, 2013, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Vol. 19, No. 4.

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Rozenberg, V.L. Problem of reconstructing a disturbance in a linear stochastic equation: The case of incomplete information. Proc. Steklov Inst. Math. 287 (Suppl 1), 167–174 (2014). https://doi.org/10.1134/S0081543814090168

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  • DOI: https://doi.org/10.1134/S0081543814090168

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