Abstract.
We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are determined. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also given.
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Mathematics Subject Classification (2000):Primary 60G17, 60J60, Secondary 28A80, 30C35, 60G52, 60J50
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Benjamini, I., Chen, ZQ. & Rohde, S. Boundary trace of reflecting Brownian motions. Probab. Theory Relat. Fields 129, 1–17 (2004). https://doi.org/10.1007/s00440-003-0318-7
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DOI: https://doi.org/10.1007/s00440-003-0318-7
Key words or phrases
- Reflecting Brownian motion
- Hausdorff dimension
- Uniform dimensional result
- Boundary occupation time
- Boundary trace
- Conformal mapping