Some Markov processes with Brownian exit distributions (Q1805001)

Let \(D\) be a bounded domain in \(\mathbb{R}^ d\) with regular boundary and let \(X = (X_ t, P^ \times)\) be a standard Markov process in \(D\) with continuous paths up to its lifetime. It is shown that, under some additional conditions on \(X\), it is possible to add a nonlocal part to its generator and construct the corresponding standard Markov process in \(D\) having Brownian exit distributions from \(D\).