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On some functional inequalities for skew Brownian motion A. T. Abakirova Laboratoire de Mathématiques Paul Painlevé, Université Lille 1, 59 655 Villeneuve d'Ascq Cedex, France Abstract: We study the Poincaré and logarithmic Sobolev inequalities. We provide several constructions of skew Brownian motion; this is an example of diffusion with singular drift interesting from different points of view. We obtain inequalities for skew Brownian motion that naturally generalize the Gaussian case. It turns out that for skew Brownian motion the estimates depend on the local time of the process. DOI: https://doi.org/10.1134/S0371968514040025   Full text:
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English version: Proceedings of the Steklov Institute of Mathematics, 2014, 287:1, Bibliographic databases:    Document Type: Article UDC: 519.21 Received in March 2014 Citation: A. T. Abakirova, “On some functional inequalities for skew Brownian motion”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 
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