This article is cited 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.

UDC: 517.977

Received: 31.05.2013

 English version: Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2014, 287, suppl. 1, S167–S174

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