Effect of Additive Perturbations on the Solution of Reflected Backward Stochastic Differential Equations

Abstract

This chapter has as a topic large class of general, nonlinear reflected backward stochastic differential equations with a lower barrier, whose generator, final condition as well as barrier process arbitrarily depend on a small parameter. The solutions of these equations which are obtained by additive perturbations, named the perturbed equations, are compared in the L p -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 L p -stable are given. It is shown that for an arbitrary a > 0 there exists t a ≤ T , such that the L p -difference between the solutions of both the perturbed and unperturbed equations is less than a for every t ∈ t a T .