Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with neumann boundary conditions

Abstract

In this paper we explicit the derivative of the flows of one-dimensional reflected diffusion processes. We then get stochastic representations for derivatives of viscosity solutions of one-dimensional semilinear parabolic partial differential equations and parabolic variational inequalities with Neumann boundary conditions. © Association des Publications de l'Institut Henri Poincaré, 2011.