Abstract : 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 parabolic
semilinear PDE which naturally appears when the underlying filtration
is Brownian. We consider two aspects of well-posedness for
the Pseudo-PDEs: "classical" and "martingale" solutions.
