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 $L^p$ ‐sense, $p=2$ , with the solutions of the appropriate unperturbed equations of the equal type. More precisely, we prove that for an arbitrary $\eta >0$ there exists an interval $[\overline{t}\left(\eta \right),T]\subset [0,T]$ on which the $L^p$ ‐difference between the solutions of perturbed and unperturbed equations is less than $\eta$ . 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.