Periodic solutions of systems of differential equations with random right-hand sides

• Date: 1997
• Main Authors: Danilov, V. Ya., Martynyuk, D. I., Stanzhitskii, A. N., Данилов, В. Я., Мартынюк, Д. И., Станжицкий, А. Н.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1997
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4999
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove a theorem on the existence of periodic solutions of a system of differential equations with random right-hand sides and small parameter of the form dx/dt=εX(t, x, ξ(t)) in a neighborhood of the equilibrium state of the averaged deterministic system dx/dt=εX 0(t).