Let \((\mathbb {P}^{s,x})_{(s,x)\in [0,T]\times E}\) be a family of probability measures, where E is a Polish space, defined on the canonical probability space \({\mathbb D}([0,T],E)\) of E-valued càdlàg functions. We suppose that a martingale problem with respect to a time-inhomogeneous generator a is well-posed. We consider also an associated semilinear Pseudo-PDE for which we introduce a notion of so-called decoupled mild solution and study the equivalence with the notion of martingale solution introduced in a companion paper. We also investigate well-posedness for decoupled mild solutions and their relations with a special class of backward stochastic differential equations (BSDEs) without driving martingale. The notion of decoupled mild solution is a good candidate to replace the notion of viscosity solution which is not always suitable when the map a is not a PDE operator.

令\（（\ mathbb {P} ^ {s，x}）_ {（s，x）\ in [0，T] \ times E} \）是几类概率测度，其中E是波兰语空间，定义在E值càdlàg函数的规范概率空间\（{\ mathbb D}（[0，T]，E）\）上。我们假设关于时间不均匀的生成器a的mar问题是恰当的。我们还考虑了相关的半线性伪PDE，为此我们引入了所谓的去耦缓和解决方案，并研究伴随论文中介绍的mar解决方案概念的等效性。我们还研究了解耦的温和解的适定性及其与一类特殊的后向随机微分方程（BSDE）的关系，而没有引起driving。解耦的温和溶液的概念很适合替换粘度溶液的概念，当图a不是PDE运算符时，粘度溶液的概念并不总是合适的。