  In this note we define and study the stochastic process $X$ in link with a
parabolic transmission operator $(A,D(A))$ in divergence form. The transmission
operator involves a diffraction condition along a transmission boundary. To
that aim we gather and clarify some results coming from the theory of Dirichlet
forms as exposed in [6] and [14] for general divergence form operators. We show
that $X$ is a semimartingale and that it is solution of a stochastic
differential equation involving partial reflections in the co-normal directions
along the transmission boundary.
