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The mean perimeter of some random plane convex sets generated by a Brownian motion

By Philippe Biane and Gérard Letac

Abstract

International audienceIf C1 is the convex hull of the curve of a standard Brownian motion in the complex plane watched from 0 to 1, we consider the convex hulls of C1 and several rotations of it and compute the mean of the length of their perimeter by elementary calculations. This can be seen geometrically as a study of the exit time by a Brownian motion from certain polytopes having the unit circle as an inscribed one

Topics: 60J65 (52A10)
Publisher: 'Springer Science and Business Media LLC'
Year: 2011
DOI identifier: 10.1007/s10959-009-0272-0
OAI identifier: oai:HAL:hal-00666863v1
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