BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space [Fonctions BV dans triplet de Gelfand et le problème de réflexion sur un ensemble convexe d'un espace de Hilbert]

摘要

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 Γ We prove the existence and uniqueness of a strong solution of this problem when Γis a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when Γ=K_α, where K_α={f∈L2(0,1)|f≥-α