Stochastic variational inequalities on non-convex domains

The objective of this work is to prove in a first step the existence and the uniqueness of a solution of the. following multivalued deterministic differential equation: {dx(t) + partial derivative(-)phi(x(t))(dt) dm(t), t > 0, x(0) = x(0), where m : R+ -> R-d is a continuous function and partial derivative(-)phi is the Frechet subdifferential of a (rho, gamma)-semiconvex function phi; the domain of phi can be non-convex, but some regularities of the boundary are required. The continuity of the map m bar right arrow x : C([0, T]; R-d) - C([0, T]; R-d) associating to the input function m the solution x of the above equation, as well as tightness criteria allows to pass from the above deterministic case to the following stochastic variational inequality driven by a multi-dimensional Brownian motion: {X-t + K-t = xi + integral F-t(0)(s, X-s)ds + integral(t)(0)G(s, X-s)dB(s), t >= 0, dK(t)(omega) is an element of partial derivative(-)phi(X-t(omega))(dt). (C) 2015 Elsevier Inc. All rights reserved.