On simultaneous hitting of membranes by two skew Brownian motions

Olga Aryasova; Andrey Pilipenko

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arXiv · 0906.1695

On simultaneous hitting of membranes by two skew Brownian motions

Olga Aryasova·Andrey Pilipenko

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Abstract

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.

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Olga Aryasova, Andrey Pilipenko. 2009-06-09. On simultaneous hitting of membranes by two skew Brownian motions. https://arxiv.org/abs/0906.1695

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