  We discuss a class of Backward Stochastic Differential Equations(BSDEs) with
no driving martingale. When the randomness of the driver depends on a general
Markov process $X$, those BSDEs are denominated Markovian BSDEs and can be
associated to a deterministic problem,called Pseudo-PDE which constitute the
natural generalization of a parabolicsemilinear PDE which naturally appears
when the underlying filtration is Brownian. We consider two aspects of
well-posedness forthe Pseudo-PDEs: "classical" and "martingale" solutions.
