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 Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 2, Pages 236–244 (Mi timm1309)

Reconstruction of external actions under incomplete information in a linear stochastic equation

V. L. Rozenberg

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

Abstract: The problem of reconstructing unknown external actions in a linear stochastic differential equation is investigated on the basis of the approach of the theory of dynamic inversion. We consider the statement when the simultaneous reconstruction of disturbances in the deterministic and stochastic terms of the equation is performed with the use of discrete information on a number of realizations of a part of coordinates of the stochastic process. The problem is reduced to an inverse problem for systems of ordinary differential equations describing the mathematical expectation and covariance matrix of the original process. A finite-step software-oriented solution algorithm based on the method of auxiliary controlled models is proposed. We derive an estimate for its convergence rate with respect to the number of measured realizations.

Keywords: dynamical reconstruction, stochastic differential equation, controlled model.

DOI: https://doi.org/10.21538/0134-4889-2016-22-2-236-244

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, 296, suppl. 1, 196–205

Bibliographic databases:

UDC: 517.977
MSC: 49K15, 60H10, 93E12

Citation: V. L. Rozenberg, “Reconstruction of external actions under incomplete information in a linear stochastic equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 236–244; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 196–205

Citation in format AMSBIB
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