On representations of solutions of 1–dimensional stochastic differential equations with reflecting boundary conditions

Abstract

In this paper we give representations of the solution of 1–dimensional stochastic differential equation (SDE for short) with reflecting barrieres. To this we construct the solution of deterministic Skorohod equation with two reflecting boundaries and show which can be expressed by the operator “sup inf”. Then the solution of given SDE can be represented by a form that depend on a reflecting Brownian motion determined by solving the deterministic Skorohod eqyation