Abstract
Viability theory is a mathematical theory that offers mathematical metaphors of evolution of macrosystems arising in biology, economics, cognitive sciences, games, and similar areas, as well as in nonlinear systems of control theory. The viability problem has been studied by many authors by using various frameworks and techniques and is still one of the active directions of differential equations. The viability property in a stochastic framework was explored first by Aubin and Da Prato (Aubin & Da Prato, 1990). In this paper, we give a necessary condition for viability results of an impulsive stochastic functional differential equation driven by a fractional Brownian motion with Hurst parameter 1/2 < H <1.
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