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

A probabilistic approach to a non-local quadratic form and its connection to the Neumann boundary condition problem