Is a Brownian Motion Skew?. (4th October 2013)

• Record Type: Journal Article
• Authors: Lejay, Antoine; Mordecki, Ernesto; Torres, Soledad
• Is Part Of: Scandinavian journal of statistics. Volume 41:Number 2(2014:Jun.)
• Page Start: 346
• Page End: 364
• Publication Date: 2013-10-04
• Subjects: Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12033
• Languages: English
• ISSNs: 0303-6898

Abstract

<abstract abstract-type="main" id="sjos12033-abs-0001"> <title>ABSTRACT</title> <p id="sjos12033-para-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.</p> </abstract>