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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 4, 2001, pp. 817–844
DOI: 10.4171/ZAA/1047

Published online: 2001-12-31

Lipschitz Continuity of Polyhedral Skorokhod Maps

Pavel Krejcí[1] and A.A. Vladimirov[2]

(1) Academy of Sciences, Praha, Czech Republic
(2) Institute for Information Transmission Problems, Moscow, Russian Federation

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.

Keywords: Polyhedral Skorokhod problem, oblique reflections, Lipschitz continuity

Krejcí Pavel, Vladimirov A.A.: Lipschitz Continuity of Polyhedral Skorokhod Maps. Z. Anal. Anwend. 20 (2001), 817-844. doi: 10.4171/ZAA/1047