Abstract
A notion of strong 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.
| Original language | English |
|---|---|
| Pages (from-to) | 219-243 |
| Number of pages | 25 |
| Journal | Potential Analysis |
| Volume | 2 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sept 1993 |
| Externally published | Yes |
Keywords
- Brownian motion
- Caccioppoli set
- Dirichlet form
- Mathematics Subject Classifications (1991): Primary 60J65, secondary 60J60, 60J55, 49Q15, 31C25
- Skorokhod decomposition
- quasimartingale
- reflecting symmetric diffusion
- set of finite perimeter
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Chen, Z. Q., Fitzsimmons, P. J., & Williams, R. J. (1993). Reflecting Brownian motions: Quasimartingales and strong Caccioppoli sets. Potential Analysis, 2(3), 219-243. https://doi.org/10.1007/BF01048506