REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH PERTURBATIONS

This paper deals with a large class of reflected backward stochastic differential equations whose generators arbitrarily depend on a small parameter. The solutions of these equations, named the perturbed equations, are compared in the L-p-sense, p is an element of]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 L-p-stable are given. It is shown that for an arbitrary eta > 0 there exists an interval [t(eta), T] subset of [0, T] on which the L-p-difference between the solutions of both the perturbed and unperturbed equations is less than eta.