A Skorokhod Problem Governed by a Closed Convex Moving Set

Charles Castaing; Manuel D. P. Monteiro Marques; Paul Raynaud de Fitte

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Charles Castaing

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

charles.castaing@gmail.com

Manuel D. P. Monteiro Marques

Dep. de Matemática, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

mdmarques@fc.ul.pt

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

prf@univ-rouen.fr

Keywords

Bounded variation
differential measure
normal cone
Skorokhod problem
sweeping process
stochastic differential equation
martingale solution
Young measure

Mathematics Subject Classification

34H05, 34K35, 60H10

Suggested citation

C. Castaing, M. D. P. Monteiro Marques, P. Raynaud de Fitte. “A Skorokhod Problem Governed by a Closed Convex Moving Set.” Journal of Convex Analysis 23 (2016), No. 2, 387–423.