EXISTENCE OF LYAPUNOV-KRASOVSKII FUNCTIONALS FOR STOCHASTIC FUNCTIONAL DIFFERENTIAL ITO-SKOROKHOD EQUATIONS UNDER THE CONDITION OF SOLUTIONS' STABILITY ON PROBABILITY WITH FINITE AFTEREFFECT

摘要

In the paper, it is established that Lyapunov–Krasovskii functionals with definite properties exist for dynamic systems of random structure with finite prehistory and with the property of one or another probability stability.