We show that a special stability condition of the associated system of oblique projections (the so-called -paracontractivity) guarantees that the corresponding polyhedral Skorokhod problem in a Hilbert space is solvable in the space of absolutely continuous functions with values in . 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 and . Also, an explicit upper bound for the Lipschitz constant is derived.
Cite this article
Pavel Krejčí, A.A. Vladimirov, Lipschitz Continuity of Polyhedral Skorokhod Maps. Z. Anal. Anwend. 20 (2001), no. 4, pp. 817–844DOI 10.4171/ZAA/1047