no. 2
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. 
@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},
     pages = {229--249},
     publisher = {Gauthier-Villars},
     volume = {29},
     number = {2},
     year = {1993},
     mrnumber = {1227418},
     zbl = {0777.60073},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1993__29_2_229_0/}
}
TY  - JOUR
AU  - Griffin, Philip S.
AU  - McConnell, Terry R.
AU  - Verchota, Gregory
TI  - Conditioned brownian motion in simply connected planar domains
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1993
SP  - 229
EP  - 249
VL  - 29
IS  - 2
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPB_1993__29_2_229_0/
LA  - en
ID  - AIHPB_1993__29_2_229_0
ER  - 
%0 Journal Article
%A Griffin, Philip S.
%A McConnell, Terry R.
%A Verchota, Gregory
%T Conditioned brownian motion in simply connected planar domains
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1993
%P 229-249
%V 29
%N 2
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPB_1993__29_2_229_0/
%G en
%F 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. http://archive.numdam.org/item/AIHPB_1993__29_2_229_0/

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

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

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

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

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

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

[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 | Zbl