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Journal of Convex Analysis 23 (2016), No. 2, 387--423
Copyright Heldermann Verlag 2016

A Skorokhod Problem Governed by a Closed Convex Moving Set

Charles Castaing
Dép. de Mathématiques, Université Montpellier II, Case courrier 051, 34095 Montpellier Cedex 5, France

Manuel D. P. Monteiro Marques
Dep. de Matemática, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

Paul Raynaud de Fitte
Laboratoire de Mathématiques, Université de Rouen, Avenue de l'Université, BP.12, Technopôle du Madrillet, F-76801 Saint-Étienne-du-Rouvray

We present several results in Skorokhod problems governed by a sweeping process with application to a Skorokhod differential equation in both deterministic and stochastic cases. In particular, we study a Skorokhod evolution inclusion involving the normal cone of a closed convex moving set with nonempty interior via Young measures.

Keywords: Bounded variation, differential measure, normal cone, Skorokhod problem, sweeping process, stochastic differential equation, martingale solution, Young measure.

MSC: 34H05, 34K35, 60H10

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