Abstract
A notion ofstrong Caccioppoli set is defined for bounded Euclidean domains. It is shown that stationary (normally) reflecting Brownian motion on the closure of a bounded Euclidean domain is a quasimartingale on each compact time interval if and only if the domain is a strong Caccioppoli set. A similar result is shown to hold for symmetric reflecting diffusion processes.
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Research supported in part by NSF Grant DMS 91-01675.
Research supported in part by NSF Grants DMS 86-57483 and 90-23335.
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Chen, Z.Q., Fitzsimmons, P.J. & Williams, R.J. Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets. Potential Anal 2, 219–243 (1993). https://doi.org/10.1007/BF01048506
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DOI: https://doi.org/10.1007/BF01048506