Abstract. Using the second Lyapunov–Krasovskii method, sufficient conditions are obtained for the asymptotic stochastic global stability, global stability, and mean-square stability of trivial solutions to systems of diffusion stochastic functional-differential equations with Markovian switchings, and the theory is illustrated by giving two model problems.
Keywords: stochastic dynamic system, hereditary system, Markov perturbation.
Ясинский Владимир Кириллович,
доктор физ.-мат. наук, профессор Черновицкого национального университета имени Юрия Федьковича,
e-mail: yasinsk@list.ru.