Weak convergence of censored and reflected stable processes

It is shown that if a sequence of open n -sets D k increases to an open n -set D then reflected stable processes in D k converge weakly to the reflected stable process in D for every starting point x in D . The same result holds for censored α -stable processes for every x in D if D and D k satisfy the uniform Hardy inequality. Using the method in the proof of the above results, we also prove the weak convergence of reflected Brownian motions in unbounded domains.