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On the expected exit time of planar Brownian motion from simply connected domains

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	On the expected exit time of planar Brownian motion from simply connected domains
2.	Creator	Author's name, affiliation, country	Greg T. Markowsky; Monash University
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Brownian motion; exit time; conformal maps
3.	Subject	Subject classification	60J65, 30C35
4.	Description	Abstract	In this note, we explore applications of a known lemma which relates the expected exit time of Brownian motion from a simply connected domain with the power series of a conformal map into that domain. We use the lemma to calculate the expected exit time from a number of domains, and in the process describe a probabilistic method for summing certain series. In particular, we give a proof of Euler's classical result that $\zeta(2) = \pi^2/6$. We also show how the relationship between the power series and the Brownian exit time gives several immediate consequences when teamed with a deep result of de Branges concerning the coefficients of power series of normalized conformal maps. We conclude by stating an extension of the lemma in question to domains which are not simply connected.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Australian Research Council Grant DP0988483
7.	Date	(YYYY-MM-DD)	2011-10-26
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1653
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1653
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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