We show the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite q-variation with q∈[1,2). In contrast to previous work, we apply a direct fixpoint argument and do not rely on any type of flow decomposition. The resulting object is an effective tool to study semilinear rough partial differential equations via a Feynman–Kac type representation.

中文翻译：

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杨氏漂移的倒向随机微分方程

我们显示了倒向随机微分方程的适定性，该方程包含一个由带有q∈[1,2）的有限q变量路径驱动的附加漂移。与以前的工作相反，我们应用直接定点参数，并且不依赖于任何类型的流分解。生成的对象是通过Feynman-Kac类型表示法研究半线性粗糙偏微分方程的有效工具。