The paper investigates the problem of realizing a prescribed solution of a linear stochastic differential equation subject to an unknown disturbance and a control to be determined. Essentially, it is required to develop an algorithm for suppressing the disturbance by means of an appropriate control based on discrete information about a certain number of realizations of the random process. Under the designed control, the solution of the original equation must track, in a weak metric, the solution of a reference equation of the same structure but without disturbance and control. Using the method of moments, the problem is reduced to realizing a certain solution of a system of ordinary differential equations describing the mathematical expectation and covariance matrix of the original process. The applicability of a feedback control algorithm previously developed for ordinary differential equations is justified, and a corresponding modification is proposed, for which the accuracy is estimated with respect to the number of measurable realizations available. A model example illustrating the constructiveness of the algorithm is given.
Keywords: stochastic differential equation, disturbance reduction, method of moments
Received April 30, 2026
Revised May 14, 2026
Accepted May 18, 2026
Valeriy Lvovich Rozenberg, Cand. Sci. (Phys.-Math.), Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620077 Russia, e-mail: rozen@imm.uran.ru
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Cite this article as: V.L. Rozenberg. On realization of a prescribed solution to a linear stochastic differential equation. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 2, pp. 221–230.
