Exact inequalities for a maximum of slanted Brownian motion / Ya. A. Lyul'ko. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 4. P. 28-31 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

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.

Key words: skew Brownian motion, maximal inequalities, optimal stopping rules, local time.