Robust Analysis of Perturbed Backward Doubly Stochastic Differential Equations
J. Đorđević (Djordjevic)
2025, v.31, Issue 1, 21-54
ABSTRACT
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.
Keywords: backward doubly stochastic differential equations, perturbations, L^p-stability, L^p-closeness, Bihari's inequality
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