The Mean Perimeter of Some Random Plane Convex Sets Generated by a Brownian Motion

Philippe Biane () and Gérard Letac ()
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Philippe Biane: Université Paris-Est
Gérard Letac: Université Paul Sabatier

Journal of Theoretical Probability, 2011, vol. 24, issue 2, 330-341

Abstract: Abstract If C 1 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 C 1 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.

Keywords: Stopping times; Exit times; Random convex sets; Brownian motion; 60J65; 52A10 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-009-0272-0

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