This article is cited in 6 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.

UDC: 519.626

Received: 22.10.2014
Revised: 26.10.2015

DOI: 10.7868/S0044466916030169

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:3, 367–375

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