PUB - Publikationen an der Universität Bielefeld

In this Note we Introduce BV functions in a Gelfand triple which is an extension of BV functions in Ambrosio et al preprint [1] by using Dirichlet form theory By this definition we can consider the stochastic reflection problem associated with a self adjoint operator A and a cylindrical Wiener process on a convex set Gamma We prove the existence and uniqueness of a strong solution of this problem when Gamma is a regular convex set The result is also extended to the non symmetric case Finally we extend our results to the case when Gamma = K-alpha where K-alpha = {f is an element of L-2(0 1) vertical bar f >= -alpha} alpha >= 0 (C) 2010 Academie des sciences Published by Elsevier Masson SAS All rights reserved