Bañuelos, Rodrigo; Carroll, Tom
Extremal problems for conditioned brownian motion and the hyperbolic metric
Annales de l'institut Fourier, Tome 50 (2000) no. 5 , p. 1507-1532
Zbl 0963.31001 | MR 2002k:31003
doi : 10.5802/aif.1798
URL stable : http://www.numdam.org/item?id=AIF_2000__50_5_1507_0

Cet article étudie les inégalités de type isopérimétrique pour le mouvement brownien conditionné et leurs généralisations en termes de la métrique hyperbolique. En particulier, on prouve une généralisation d’une inégalité de P. Griffin, T. McConnell et G. Verchota concernant des domaines extrémaux pour le temps de vie du mouvement brownien conditionné dans des domaines simplement connexes. L’inégalité de limite inférieure qui y correspond est formulée sous différentes formes équivalentes, et un de leur cas particuliers est démontré.
This paper investigates isoperimetric-type inequalities for conditioned Brownian motion and their generalizations in terms of the hyperbolic metric. In particular, a generalization of an inequality of P. Griffin, T. McConnell and G. Verchota, concerning extremals for the lifetime of conditioned Brownian motion in simply connected domains, is proved. The corresponding lower bound inequality is formulated in various equivalent forms and a special case of these is proved.

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