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On the convex hull of a Brownian excursion with parabolic drift

By Christophe Giraud


AbstractThe solutions of Burgers equation with white noise initial velocity are closely connected to the convex hull Ha of a Brownian excursion with parabolic drift s↦es+a2s2. We derive from the law of the minimum σ and the location η of the minimum of s↦2es/s(1−s) a complete description of the convex hull Ha. As an application, we determine the statistical properties of the Burgers turbulence on the circle

Publisher: Elsevier Science B.V.
Year: 2003
DOI identifier: 10.1016/S0304-4149(03)00027-9
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