JournalszaaVol. 20, No. 4pp. 817–844

Lipschitz Continuity of Polyhedral Skorokhod Maps

  • Pavel Krejčí

    Academy of Sciences, Praha, Czech Republic
  • A.A. Vladimirov

    Institute for Information Transmission Problems, Moscow, Russian Federation
Lipschitz Continuity of Polyhedral Skorokhod Maps cover
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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 XX is solvable in the space of absolutely continuous functions with values in XX. 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)C([0, T];X) and W1,1(0,T;X)W^{1,1} (0, T; X). 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. 817–844

DOI 10.4171/ZAA/1047