I. S. Maksimova, K. Yu. Osipenko, “Optimal recovery of a solution of a system of linear differential equations from initial information given with a random error”, Mat. Sb., 2025, Volume 216, Number 4,Pages <nobr>67

Optimal recovery of a solution of a system of linear differential equations from initial information given with a random error

I. S. Maksimova^a, K. Yu. Osipenko^bc

^a Faculty of Physical, Mathematical and Natural Sciences, RUDN University, Moscow, Russia
^b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia

Abstract: The problem of the optimal recovery of a solution of a system of linear differential equations from initial information containing a random error is considered. Optimal methods are searched for among all possible (not necessarily linear) recovery methods. Depending on the given variance of random errors, the optimal recovery methods constructed in the paper, which turn out to be linear, use only part of the available information.
Bibliography: 17 titles.

Keywords: optimal recovery, systems of linear differential equations, information with random errors.

MSC: Primary 34A45, 41A65, 42A05; Secondary 41A46

Received: 19.04.2024 and 06.09.2024

DOI: 10.4213/sm10109