  We focus on a class of BSDEs driven by a cadlag martingale and corresponding
Markov type BSDE which arise when the randomness of the driver appears through
a Markov process. To those BSDEs we associate a deterministic problem which,
when the Markov process is a Brownian diffusion, is nothing else but a
parabolic type PDE. The solution of the deterministic problem is intended as
decoupled mild solution, and it is formulated with the help of a
time-inhomogeneous semigroup.
