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Exact inequalities for the maximum of a skew Brownian motion

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Abstract

The maximal inequality for the skew Brownian motion being a generalization of the well-known inequalities for the standard Brownian motion and its module is obtained in the paper. The proof is based on the solution to an optimal stopping problem for which we find the cost function and optimal stopping time.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    Ya. A. Lyul’ko

Authors
  1. Ya. A. Lyul’ko
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Additional information

Original Russian Text © Ya.A. Lyul’ko, 2012, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2012, Vol. 67, No. 4, pp. 26–31.

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Lyul’ko, Y.A. Exact inequalities for the maximum of a skew Brownian motion. Moscow Univ. Math. Bull. 67, 164–169 (2012). https://doi.org/10.3103/S0027132212040055

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  • DOI: https://doi.org/10.3103/S0027132212040055

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