Perturbed backward stochastic differential equations

The paper discusses a large class of backward stochastic differential equations whose coefficients additively depend on small perturbations. Their solutions are compared in the LpLp-sense, p≥2p≥2, with the solutions of the appropriate unperturbed equations of the equal type. More precisely, we prove that for an arbitrary η>0η>0 there exists an interval [t̄(η),T]⊂[0,T] on which the LpLp-difference between the solutions of perturbed and unperturbed equations is less than ηη. In contrast to similar problems about various perturbed forward stochastic differential equations, a completely different procedure must be applied on perturbed backward stochastic differential equations.