Traps for reflected Brownian motion

Krzysztof Burdzy; Zhen Qing Chen; Donald E. Marshall

doi:10.1007/s00209-005-0849-y

Traps for reflected Brownian motion

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

^*Corresponding author for this work

University of Washington

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	103-132
Number of pages	30
Journal	Mathematische Zeitschrift
Volume	252
Issue number	1
DOIs	https://doi.org/10.1007/s00209-005-0849-y
Publication status	Published - Jan 2006
Externally published	Yes

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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

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Traps for reflected Brownian motion

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