  This note develops shortly the theory of time-inhomogeneous additive
functionals and is a useful support for the analysis of time-dependent Markov
processes and related topics. It is a significant tool for the analysis of
BSDEs in law. In particular we extend to a non-homogeneous setup some results
concerning the quadratic variation and the angular bracket of Martin-gale
Additive Functionals (in short MAF) associated to a homogeneous Markov
processes.

Probability