Expected exit times of Brownian motion from planar domains: Complements to a paper of Markowsky

Abstract

We supplement a very recent paper of G. Markowsky concerned with the expected exit times of Brownian motion from planar domains. Besides the use of conformal mapping, we apply results from potential theory. We treat the case of a wedge-shaped region exactly, subsuming an example of Markowsky. A number of other results are presented, including for a half disc, $n$-grams, and a variety of other regions.

arXiv comment30 pages, 7 figures

References in corpus (1)

• The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing

Cited by in corpus (1)

• Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian