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Theory of Stochastic Processes, 2009, Volume 15(31), Issue 1, paper published in the English version journal (Mi thsp106)  
On simultaneous hitting of membranes by two skew Brownian motions

O. V. Aryasovaa, A. Yu. Pilipenkob

a Institute of Geophysics, National Academy of Sciences of Ukraine, Palladina Pr., 32, Kiev 03680, Ukraine
b Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska Str., 3, Kiev 01601, Ukraine
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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.
Keywords: Skew Brownian motion, singular SDE.
Bibliographic databases:
Document Type: Article
MSC: 60J65, 60H10
Language: English
Citation: O. V. Aryasova, A. Yu. Pilipenko
Citation in format AMSBIB
\Bibitem{AryPil09}
\by O.~V.~Aryasova, A.~Yu.~Pilipenko
\mathnet{http://mi.mathnet.ru/thsp106}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2603165}
\zmath{https://zbmath.org/?q=an:1224.60211}
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