Is a Brownian Motion Skew?

Antoine Lejay, Ernesto Mordecki and Soledad Torres

Scandinavian Journal of Statistics, 2014, vol. 41, issue 2, 346-364

Abstract: type="main" xml:id="sjos12033-abs-0001"> We study the asymptotic behaviour of the maximum likelihood estimator corresponding to the observation of a trajectory of a skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non-classical, under the null hypothesis of the skew Brownian motion being an usual Brownian motion. This allows to design a test on the skewness parameter. We show that numerical simulations can be easily performed to estimate the skewness parameter and provide an application in Biology.

Date: 2014
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