On the strong solutions of one-dimensional stochastic differential equations with reflecting boundary (Q1318336)

One-dimensional stochastic differential equations with reflecting boundary condition are investigated. The existence and uniqueness of strong solutions are proved under the assumptions of non-degenerate smooth diffusion coefficient and measurable drift coefficient. Wong-Zakai type approximation of the solution is also derived. The existence proof is based on a known result in the case of (locally) Lipschitz drift and constant non-degenerate diffusion. It extends to the general case by approximations, use of a comparison theorem and change of variables. The (strong) uniqueness result deals with the local time and a known result on uniqueness in law.