Abstract
In this paper we investigate the reflected symmetric α-stable processes and their generators. We show that the generators are regional fractional Laplacians on the closed region. In the case of 1≤α<2 their existence requires that on the boundary. Among other things we obtain the integration by parts formula of the regional fractional Laplacian and the semi-martingale decomposition of the reflected symmetric α-stable processes.
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Guan, QY., Ma, ZM. Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian. Probab. Theory Relat. Fields 134, 649–694 (2006). https://doi.org/10.1007/s00440-005-0438-3
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DOI: https://doi.org/10.1007/s00440-005-0438-3