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JOURNALS // Contemporary Mathematics. Fundamental Directions // Archive

CMFD, 2022 Volume 68, Issue 4, Pages 621–634 (Mi cmfd477)

This article is cited in 1 paper

On a system of differential equations with random parameters

V. G. Zadorozhniy, G. S. Tikhomirov

Voronezh State University, Voronezh, Russia

Abstract: An explicit formula for the mathematical expectation and second moment functions of a solution to a linear system of ordinary differential equations with a random parameter and a vector random right-hand side is obtained. The problem is reduced to the deterministic Cauchy problem for systems of first-order linear partial differential equations. We obtain an explicit formula for a solution of linear systems of partial differential equations of the first order with constant coefficients. An example is given showing that random factors can have a stabilizing effect on a linear system of differential equations.

Keywords: linear system of ordinary differential equations with a random parameter and a vector random right-hand side, moment functions, system of first-order linear partial differential equations, explicit solution.

UDC: 517.972

DOI: 10.22363/2413-3639-2022-68-4-621-634



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© Steklov Math. Inst. of RAS, 2024