Problem of reconstructing a disturbance in a linear stochastic equation: The case of incomplete information |
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Authors: | V L Rozenberg |
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Institution: | 1.Institute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences,Yekaterinburg,Russia |
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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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