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

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. © 2025 Russian Academy of Sciences, Steklov Mathematical Institute of RAS.