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Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets (1993)

Chen, Z. Q. ; Fitzsimmons, P. J. ; Williams, R. J.

Springer

Potential analysis 2 (1993), S. 219-243

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ISSN: 1572-929X

Keywords: Primary 60J65 ; secondary 60J60, 60J55, 49Q15, 31C25 ; Brownian motion ; reflecting symmetric diffusion ; Dirichlet form ; Caccioppoli set ; set of finite perimeter ; quasimartingale ; Skorokhod decomposition

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01048506

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