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Let $(\mathbb{P}^{s,x})_{(s,x)\in[0,T]\times E}$ be a family of probabilitymeasures, where $E$ is a Polish space,defined on the canonical probabilityspace ${\mathbb D}([0,T],E)$ of $E$-valued cadlag functions. We suppose that amartingale problem with respect to a time-inhomogeneous generator $a$ iswell-posed. We consider also an associated semilinear {\it Pseudo-PDE} withgenerator $a$ for which we introduce a notion of so called {\it decoupled mild}solution and study the equivalence with the notion of martingale solutionintroduced in a companion paper. We also investigate well-posedness fordecoupled mild solutions and their relations with a special class of BSDEswithout driving martingale. The notion of decoupled mild solution is a goodcandidate to replace the notion of viscosity solution which is not alwayssuitable when the map $a$ is not a PDE operator.

BSDEs with no driving martingale, Markov processes and associated Pseudo  Partial Differential Equations. Part II: Decoupled mild solutions and  Examples