C&SA | Contents

Volume 54 >>> № 6 NOVEMBER — DECEMBER 2018

UDC 519.217:519.718:519.837

I.V. Yurchenko¹, V.K. Yasynskyy²

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

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

Keywords: systems of random structure, aftereffect, stability, Lyapunov–Krasovskii functionals.

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¹ Yu. Fedkovych National University, Chernivtsi, Ukraine

i.yurchenko@chnu.edu.ua

² Yu. Fedkovych National University, Chernivtsi, Ukraine

v.yasynskyy@chnu.edu.ua

UDC 519.217:519.718:519.837

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

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