Lipschitz Continuity of Polyhedral Skorokhod Maps

Abstract

We show that a special stability condition of the associated system of oblique projections (the so-called $\ell$-paracontractivity) guarantees that the corresponding polyhedral Skorokhod problem in a Hilbert space $X$ is solvable in the space of absolutely continuous functions with values in $X$. If moreover the oblique projections are transversal, the solution exists and is unique for each continuous input and the Skorokhod map is Lipschitz continuous in both spaces $C([0,T];X)$ and $W^{1,1}(0,T;X)$. Also, an explicit upper bound for the Lipschitz constant is derived.