The Viability Property for Path-dependent SDE under Open Constraints

In this note, we study the viability of a bounded open domain in $\mathbb{R}$ 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 [\textit{Indiana Univ. Math. J.} \textbf{59} (2010) 53-78] to a non-Markovian setting.

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