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Is a Brownian Motion Skew?

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ABSTRACT

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.

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