Viability for stochastic functional differential equations in Hilbert spaces driven by fractional Brownian motion

In this paper, we consider a class of stochastic functional differential equations in Hilbert spaces driven by a fractional Brownian motion with Hurst parameter 1/2 < H < 1. By using pathwise approach, we prove a global existence and uniqueness result of the mild solution for the equations considered under some local Lipschitz conditions. Subsequently, by establishing some new estimates, we also prove some viability results to the stochastic systems under investigation.