Conditions of convergence in mean of skew Brownian motions with local times at several points that are contracted into a limit point are obtained. It is proved that the limit process is also a skew Brownian motion with local time at the limit point. A formula to calculate the coefficient of the local time of the limit process is given.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 13, No. 2, pp. 213–223 April–June, 2016.
Translated from Ukrainian by V. V. Kukhtin
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Krykun, I.H. Convergence of skew Brownian motions with local times at several points that are contracted into a single one. J Math Sci 221, 671–678 (2017). https://doi.org/10.1007/s10958-017-3258-y