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Journal Articles Scandinavian Journal of Statistics Year : 2014

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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Dates and versions

inria-00544442 , version 1 (14-12-2010)
inria-00544442 , version 2 (26-02-2013)
inria-00544442 , version 3 (21-05-2013)
inria-00544442 , version 4 (19-07-2013)

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Cite

Antoine Lejay, Ernesto Mordecki, Soledad Torres. Is a Brownian motion skew?. Scandinavian Journal of Statistics, 2014, 5 (2), pp.346-364. ⟨10.1111/sjos.12033⟩. ⟨inria-00544442v4⟩
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