  In this paper, we look at a probabilistic approach to a non-local quadratic
form that has lately attracted some interest. This form is related to a
recently introduced non-local normal derivative. The goal is to construct two
Markov process: one corresponding to that form and the other which is related
to a probabilistic interpretation of the Neuman problem. We also study the
Dirichlet-to-Neumann operator for non-local operators.
