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In this article, we aim to present the Carathéodory scheme for a class of perturbed stochastic differential equations with reflecting boundary (PSDERB). It is shown that the Carathéodory approximate solutions converge to the unique solution of this class of PSDERB. The existence and pathwise uniqueness theorem for this class of PSDERB are established under irregular coefficients.

Carathéodory approximate solutions for a class of perturbed reflected stochastic differential equations with irregular coefficients