Conditioned brownian motion in simply connected planar domains
Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) no. 2, p. 229-249
@article{AIHPB_1993__29_2_229_0,
     author = {Griffin, Philip S. and McConnell, Terry R. and Verchota, Gregory},
     title = {Conditioned brownian motion in simply connected planar domains},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {29},
     number = {2},
     year = {1993},
     pages = {229-249},
     zbl = {0777.60073},
     mrnumber = {1227418},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1993__29_2_229_0}
}
Griffin, Philip S.; McConnell, Terry R.; Verchota, Gregory. Conditioned brownian motion in simply connected planar domains. Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) no. 2, pp. 229-249. https://www.numdam.org/item/AIHPB_1993__29_2_229_0/

[1] C. Bandle, Isoperimetric inequalities and applications, Pitman Publishing, Boston, 1980. | MR 572958 | Zbl 0436.35063

[2] R. Bañuelos, On the estimate of Cranston and McConnell for elliptic diffusions in uniform domains, Prob. Th. Rel. Fields, Vol. 76, 1987, pp. 311-323. | MR 912657 | Zbl 0611.60071

[3] R. Bañuelos and T. Carrol, Conditional Brownian motion and hyperbolic geodesics in simply connected domains, (Preprint).

[4] E.F. Beckenbach and T. Rado, Subharmonic functions and surfaces of negative curvature, Trans. Amer. Math. Soc., Vol. 35, 1933, pp. 662-674. | MR 1501708 | Zbl 0007.13001

[5] T. Carleman, Zur Theorie der Minimalflächen, Math Z., Vol. 9, 1921, pp. 154-160. | JFM 48.0590.02 | MR 1544458

[6] M. Cranston and T.R. Mcconnell, The lifetime of conditioned Brownian motion, Z. Warsch. Verw. Gebiete, Vol. 65, 1983, pp. 1-11. | MR 717928 | Zbl 0506.60071

[7] J.L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer, New York, 1984. | MR 731258 | Zbl 0549.31001

[8] G. Hardy J.E. Littlewood, and G. Pólya, Inequalities, 2nd Ed., Cambridge University Press, Cambridge, 1952. | MR 46395 | Zbl 0047.05302

[9] Y. Katznelson, An Introduction to Harmonic Analysis, 2nd Ed., Dover, New York, 1976. | MR 422992 | Zbl 0352.43001

[10] P. Koosis, Introduction to Hp spaces, Cambridge University Press, Cambridge, 1980. | MR 1669574 | Zbl 0435.30001

[11] T.R. Mcconnell, A conformal inequality related to the conditional gauge theorem, Trans. Amer. Math. Soc., Vol. 318, 1990, pp. 721-733. | MR 957083 | Zbl 0705.60063

[12] S. Saks and A. Zygmund, Analytic Functions, 3rd Ed., American Elsevier Publishing Co., New York, 1971. | MR 349963

[13] T. Salisbury, A Martin boundary in the plane, Trans. Amer. Math. Soc., Vol. 293, 1986, pp. 623-642. | MR 816315 | Zbl 0591.60074

[14] W.A. Veech, A Second Course in Complex Analysis, W. A. BENJAMIN Ed., Inc., New York, 1967. | MR 220903 | Zbl 0145.29901

[15] J. Xu, The lifetime of conditioned Brownian motion in planar domains of finite area, Prob. Theory Related Fields, Vol. 87, 1991, pp. 469-487. | MR 1085178 | Zbl 0718.60092