Robust Analysis of Perturbed Backward Doubly Stochastic Differential Equations

A large class of backward doubly stochastic differential equations whose coefficients are linearly perturbed is observed in this paper. Their solutions are compared in the L^p-sense (p ≥ 2) with the solutions of the appropriate unperturbed equations of the same type, under the most global non-Lipschitz condition for the coefficients of the equations. Also, an interval [t̅(η), T] ⊂ [0, T], on which the L^p difference between the solutions of perturbed and unperturbed equations is less than a given value η, is established.