Lipschitz continuity of polyhedral Skorokhod maps
- Krejčí, Pavel
- Vladimirov, Alexander A.
2010 Mathematics Subject Classification
- 47H30 52B70
- polyhedral Skorokhod problem, oblique reflections, Lipschitz continuity
We show that a special stability condition of the associated system of oblique projections (the so-called ℓ-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 C([0,T]; X) and W1,1(0,T; X). An explicit upper bound for the Lipschitz constant is derived.
- Z. Anal. Anwendungen (J. Anal. Appl.) 20 (2001), pp. 817--844