Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets |
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| Authors: | Z Q Chen P J Fitzsimmons R J Williams |
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| Institution: | (1) Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, 92093-0112 La Jolla, California, USA |
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| 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.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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| Keywords: | Primary 60J65 secondary 60J60 60J55 49Q15 31C25 |
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