Is a Brownian motion skew?

Abstract : We study the asymptotic behavior 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 that can be easily performed to estimate the skewness parameter, and provide an application in Biology.
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Antoine Lejay, Ernesto Mordecki, Soledad Torres. Is a Brownian motion skew?. Scandinavian Journal of Statistics, Wiley, 2014, 5 (2), pp.346-364. ⟨10.1111/sjos.12033⟩. ⟨inria-00544442v4⟩

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