Traps for reflected Brownian motion

Krzysztof Burdzy*, Zhen Qing Chen, Donald E. Marshall

*此作品的通讯作者

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摘要

Consider an open set [InlineMediaObject not available: see fulltext.], d ≥ 2, and a closed ball [InlineMediaObject not available: see fulltext.]. Let [InlineMediaObject not available: see fulltext.] denote the expectation of the hitting time of B for reflected Brownian motion in D starting from x D. We say that D is a trap domain if [InlineMediaObject not available: see fulltext.]. A domain D is not a trap domain if and only if the reflecting Brownian motion in D is uniformly ergodic. We fully characterize the simply connected planar trap domains using a geometric condition and give a number of (less complete) results for d > 2.

源语言英语
页(从-至)103-132
页数30
期刊Mathematische Zeitschrift
252
1
DOI
出版状态已出版 - 1月 2006
已对外发布

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Burdzy, K., Chen, Z. Q., & Marshall, D. E. (2006). Traps for reflected Brownian motion. Mathematische Zeitschrift, 252(1), 103-132. https://doi.org/10.1007/s00209-005-0849-y