Problàme de Skorohod multivoque

Abstract

An existence and uniqueness result is proven for a generalization (by introduction of a multivalued maximal monotone operator) of the deterministic Skorohod problem (with normal reflection) associated with a closed convex $D$ in $\mathbb{R}^d$ . The maximal monotone operator formulation allows for drifts that blow up as one gets near the boundary. This ‘‘multivalued approach’’ clarifies the connection between nonlinear semigroup theory and the Skorohod problem. As a consequence, we discuss then the stochastic case: multivalued stochastic differential equations are thus revisited. Therefore, we give an alternative way to construct diffusions with normal reflecting boundary conditions and discontinuous, exploding drift.

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