Geodesic
Exact inequalities for the maximum of a skew Brownian motion
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2012), pp. 26-31

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The maximal inequality for the skew Brownian motion being a generalization of the well-known inequalities for the standard Brownian motion and its modulus is obtained in the paper. The proof is based on the solution to an optimal stopping problem for which we find the value function and optimal stopping time. 
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     author = {Ya. A. Lyulko},
     title = {Exact inequalities for the maximum of a skew {Brownian} motion},
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Ya. A. Lyulko. Exact inequalities for the maximum of a skew Brownian motion. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2012), pp. 26-31. http://geodesic.mathdoc.fr/item/VMUMM_2012_4_a4/