The Viability Property for Path-dependent SDE under Open Constraints

In this note, we study the viability of a bounded open domain in $$\mathbb{R}$% ^{n}$ for a process driven by a path-dependent stochastic differential equation with Lipschitz data. We extend an invariant result of Cannarsa, Da. Prato and Frankowska [$\mathit{\text{Indiana}}\mathit{\text{Univ.}}\mathit{\text{Math.}}\mathit{\text{J.}}$ $\mathbf{\text{59}}$ (2010) 53-78] to a non-Markovian setting.