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.
@article{AIF_2000__50_5_1507_0,
author = {Ba\~nuelos, Rodrigo and Carroll, Tom},
title = {Extremal problems for conditioned brownian motion and the hyperbolic metric},
journal = {Annales de l'Institut Fourier},
pages = {1507--1532},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {50},
number = {5},
year = {2000},
doi = {10.5802/aif.1798},
mrnumber = {2002k:31003},
zbl = {0963.31001},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1798/}
}
TY - JOUR AU - Bañuelos, Rodrigo AU - Carroll, Tom TI - Extremal problems for conditioned brownian motion and the hyperbolic metric JO - Annales de l'Institut Fourier PY - 2000 SP - 1507 EP - 1532 VL - 50 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1798/ DO - 10.5802/aif.1798 LA - en ID - AIF_2000__50_5_1507_0 ER -
%0 Journal Article %A Bañuelos, Rodrigo %A Carroll, Tom %T Extremal problems for conditioned brownian motion and the hyperbolic metric %J Annales de l'Institut Fourier %D 2000 %P 1507-1532 %V 50 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1798/ %R 10.5802/aif.1798 %G en %F AIF_2000__50_5_1507_0
Bañuelos, Rodrigo; Carroll, Tom. Extremal problems for conditioned brownian motion and the hyperbolic metric. Annales de l'Institut Fourier, Tome 50 (2000) no. 5, pp. 1507-1532. doi : 10.5802/aif.1798. http://www.numdam.org/articles/10.5802/aif.1798/
[1] , Conformal Invariants: Topics in Geometric Function Theory, McGraw-Hill, New York, 1973. | MR | Zbl
[2] , Isoperimetric Inequalities and Applications, Pitman, London, 1980. | MR | Zbl
[3] and , Conditioned Brownian Motion and Hyperbolic Geodesics in Simply Connected Domains, Michigan Math. J., 40 (1993), 321-332. | MR | Zbl
[4] and , An Isoperimetric-type Inequality for Integrals of Green's Functions, Michigan Math. J., 42 (1995), 603-611. | MR | Zbl
[5] , The Geometry of Discrete Groups, Graduate Texts in Mathematics 91, Springer-Verlag, New York, 1983. | MR | Zbl
[6] and , The Lifetime of Conditioned Brownian Motion, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 65 (1983), 1-11. | MR | Zbl
[7] , and , Conditioned Brownian Motion in Simply Connected Planar Domains, Ann. Inst. Henri Poincaré, 29 (1993), 229-249. | Numdam | MR | Zbl
[8] , and , Distortion of Area and Conditioned Brownian Motion, Probab. Theory Relat. Fields, 96 (1993), 385-413. | MR | Zbl
[9] , An Introduction to Harmonic Analysis, Wiley, New York, 1968. | MR | Zbl
[10] , Complex Analysis: the Geometric Viewpoint, Carus Mathematical Monographs 23, Mathematical Association of America, 1990. | MR | Zbl
[11] , Univalent Functions, Vandenhoeck and Ruprecht, Gottingen, 1975. | Zbl
[12] , The Lifetime of Conditioned Brownian Motion in Planar Domains of Infinite Area, Probab. Theory Relat. Fields, 87 (1991), 469-487. | MR | Zbl
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