On properties of Brownian reflecting flow in a wedge
Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 79-89.

Voir la notice de l'article provenant de la source Math-Net.Ru

Consider a planar Brownian flow in a wedge with oblique reflection on the sides. The necessary and sufficient conditions are obtained for the vertex to be reached by the flow.
Keywords: Stochastic flows, reflected Brownian motion.
@article{THSP_2011_17_1_a8,
     author = {Andrey Pilipenko},
     title = {On properties of {Brownian} reflecting flow in a wedge},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {79--89},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a8/}
}
TY  - JOUR
AU  - Andrey Pilipenko
TI  - On properties of Brownian reflecting flow in a wedge
JO  - Teoriâ slučajnyh processov
PY  - 2011
SP  - 79
EP  - 89
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a8/
LA  - en
ID  - THSP_2011_17_1_a8
ER  - 
%0 Journal Article
%A Andrey Pilipenko
%T On properties of Brownian reflecting flow in a wedge
%J Teoriâ slučajnyh processov
%D 2011
%P 79-89
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a8/
%G en
%F THSP_2011_17_1_a8
Andrey Pilipenko. On properties of Brownian reflecting flow in a wedge. Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 79-89. http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a8/

[1] J. M. Harrison, M. I. Reiman, “Reflected Brownian motion on an orthant”, Ann. of Probab., 9 (1981), 302–308

[2] P. Dupuis, H. Ishii, “On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications”, Stochastics, 35 (1991), 31–62

[3] S. R. S. Varadhan, R. J. Williams, “Brownian motion in a wedge with oblique reflection”, Comm. Pure Appl. Math., 38:4 (1985), 405–443

[4] Y. Kwon, R. J. Williams, “Reflected Brownian motion in a cone with radially homogeneous reflection field”, Trans. Amer. Math. Soc., 327:2 (1991), 739–780

[5] Y. Kwon, “The submartingale problem for Brownian motion in a cone with nonconstant oblique reflection”, Probab. Theory Related Fields, 92:3 (1992), 351–391

[6] Y. Kwon, “Reflected Brownian motion in a cone: semimartingale property”, Probab. Theory Rel. Fields, 101:2 (1995), 211–226

[7] R. D. DeBlassie, “The adjoint process of reflected Brownian motion in a cone”, Stochastics Rep., 71:3-4 (2001), 201–216

[8] O. Aryasova, A. Pilipenko, “On Brownian motion on the plane with membranes on rays with a common endpoint”, Random Oper. and Stoch. Equ., 17:2 (2009), 137–156

[9] K. Burdzy, “Brownian paths and cones”, Ann. Probab., 13:3 (1985), 1006–1010

[10] M. Shimura, “Excursions in a cone for two-dimensional Brownian motion”, J. Math. Kyoto Univ., 25:3 (1985), 433–443