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GENERALIZED STOCHASTIC PERTURBATION-DEPENDING DIFFERENTIAL EQUATIONS
Abstract:The paper is devoted to the generalized stochastic differential equations of the Ito? type whose coefficients are additionally perturbed and dependent on a small parameter. Their solutions are compared with the solutions of the corresponding unperturbed equations. We give conditions under which the solutions of these equations are close in the (2m)-th moment sense on finite intervals or on intervals whose length tends to infinity as the small parameter tends to zero. We also give the degree of the closeness of these solutions.
Keywords:Generalized stochastic differential equation  Small perturbations  Closeness in the (2m)-th mean  AMS Mathematics Subject Classification (1991): 60H10
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