Relying on the pathwise uniqueness property, we prove existence of the strong solution of a one-dimensional reflected stochastic delay equation driven by a mixture of independent Brownian and fractional Brownian motions. The difficulty is that on the one hand we cannot use the fixed-point and contraction mapping methods because of the stochastic and pathwise integrals, and on the other hand the non-continuity of the Skorokhod map with respect to the norms considered.

中文翻译：

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一维反射混合随机时滞微分方程强解的存在性

依靠路径唯一性，我们证明了由独立布朗运动和分数布朗运动混合驱动的一维反射随机延迟方程的强解的存在性。困难在于，一方面，由于随机积分和路径积分，我们无法使用定点和收缩映射方法；另一方面，Skorokhod 映射相对于所考虑的范数而言是不连续的。