Geodesic
On simultaneous hitting of membranes by two skew Brownian motions
Teoriâ slučajnyh processov, Tome 15 (2009) no. 1

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We consider two depending Wiener processes which have membranes at zero with different permeability coefficients. Starting from different points, the processes almost surely do not meet at any fixed point except that where membranes are situated. The necessary and sufficient conditions for the meeting of the processes are found. It is shown that the probability of meeting is equal to zero or one.
Keywords: Skew Brownian motion, singular SDE. 
@article{THSP_2009_15_1_a0,
     author = {O. V. Aryasova and A. Yu. Pilipenko},
     title = {On simultaneous hitting of membranes by two {skew
Brownian} motions},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2009_15_1_a0/}
}
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O. V. Aryasova; A. Yu. Pilipenko. On simultaneous hitting of membranes by two skew
Brownian motions. Teoriâ slučajnyh processov, Tome 15 (2009) no. 1. http://geodesic.mathdoc.fr/item/THSP_2009_15_1_a0/