Weak convergence of censored and reflected stable processes |
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Authors: | Panki Kim |
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Institution: | Department of Mathematics, Seoul National University, Seoul 151-742, Republic of Korea |
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Abstract: | It is shown that if a sequence of open n-sets Dk increases to an open n-set D then reflected stable processes in Dk 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 Dk 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. |
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Keywords: | primary 60B10 60J25 secondary 60J35 60G52 46E35 |
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