Abstract. The second Lyapunov–Krasovskii method is used to derive the sufficient conditions for the asymptotic stochastic stability in the large, global stability, exponential mean square stability of the trivial solution of the system of stochastic diffusion functional-differential equations with Markov switchings.
Keywords: dynamic system of random structure, system with aftereffect, Markov switchings.
Ясинский Владимир Кириллович, доктор физ.-мат. наук, профессор Черновицкого национального университета имени Юрия Федьковича,
e-mail: yasinsk@list.ru.