Reflected backward stochastic differential equations with perturbations

Abstract

This paper deals with a large class of refiected backward stochastic diffierential equations whose generators arbitrarily depend on a small parameter. The solutions of these equations, named the perturbed equations, are compared in the Lp-sense, p ∈]1; 2[, with the solutions of the appropriate equations of the equal type, independent of a small parameter and named the unperturbed equations. Conditions under which the solution of the unperturbed equation is Lp-stable are given. It is shown that for an arbitrary η > 0 there exists an interval [t(η), T] ⊂ [0, T] on which the Lp-diffierence between the solutions of both the perturbed and unperturbed equations is less than η.