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

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 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 a>0 there exists ta≤T, such that the Lp-difference between the solutions of both the perturbed and unperturbed equations is less than a for every t∈taT.