Let [Formula: see text] be the space of probability measures on [Formula: see text] with finite second moment. The path independence of additive functionals of McKean–Vlasov SDEs is characterized by PDEs on the product space [Formula: see text] equipped with the usual derivative in space variable and Lions’ derivative in distribution. These PDEs are solved by using probabilistic arguments developed from Ref. 2. As a consequence, the path independence of Girsanov transformations is identified with nonlinear PDEs on [Formula: see text] whose solutions are given by probabilistic arguments as well. In particular, the corresponding results on the Girsanov transformation killing the drift term derived earlier for the classical SDEs are recovered as special situations.

中文翻译：

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McKean-Vlasov SDEs 的路径无关加性泛函的空间分布 PDEs

令 [Formula: see text] 是 [Formula: see text] 上具有有限二阶矩的概率测度空间。McKean-Vlasov SDE 的加性泛函的路径独立性的特征是乘积空间上的偏微分方程 [公式：见正文]，配备空间变量中的通常导数和分布中的 Lions 导数。这些偏微分方程是通过使用参考文献开发的概率论点来解决的。2. 因此，Girsanov 变换的路径独立性在 [公式：见文本] 上用非线性 PDE 来识别，其解也由概率论据给出。特别是，Girsanov 变换的相应结果消除了先前为经典 SDE 导出的漂移项，作为特殊情况恢复。