R. I. Kadiev, A. V. Ponosov, “Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, Number 7,Pages <nobr>63

Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect

R. I. Kadiev^ab, A. V. Ponosov^c

^a Dagestan Federal Research Center of the Russian Academy of Sciences, 45 M. Hajiyev str., Makhachkala, 367000 Russia
^b Dagestan State University, 43 a M. Hajiyev str., Makhachkala, 367000, Russia
^c Norwegian University of Life Sciences, P.O. Box 5003 N-1432, As, Norway

Abstract: The paper studies the global moment stability of systems of nonlinear Itô differential equations with delays. The analysis is done by a modified regularization method, known as the $W$-method, and based on the use of some auxiliary equation with subsequent application of the theory of positively invertible matrices. Sufficient conditions for the global asymptotic moment stability for both sufficiently general and specific systems of Itô equations formulated in terms of parameters of these systems are given. Connections between this stability and the properties of the delay functions are established.

Keywords: system of stochastic differential equations, nonlinear Itô equation, stability of solutions, asymptotics of solutions, method of auxiliary equations, positive invertibility of matrices.

UDC: 517.929.4:519.21

Received: 18.05.2023
Revised: 06.06.2023
Accepted: 26.09.2023

DOI: 10.26907/0021-3446-2024-7-63-76