Perturbed Skorohod equations and perturbed reflected diffusion processes

In this paper, we obtain the existence and uniqueness of the solution to the perturbed Skorohod equation g(t) = f(t) + alpha max(0)less than or equal to(s)less than or equal to(t) g(s) + h(t) for any real constant alpha < 1 and any given continuous function f, where g greater than or equal to 0, and h is an increasing function which only increases at the time g is at zero. As an application, we establish the existence and uniqueness of some perturbed reflected diffusion processes. (C) 2004 Elsevier SAS. All rights reserved.