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Is a Brownian Motion Skew?
Author(s) -
Lejay Antoine,
Mordecki Ernesto,
Torres Soledad
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12033
Subject(s) - mathematics , estimator , skewness , brownian motion , skew , discretization , fractional brownian motion , diffusion process , weak convergence , brownian excursion , statistical physics , asymptotic distribution , mathematical analysis , geometric brownian motion , statistics , physics , knowledge management , innovation diffusion , computer security , astronomy , computer science , asset (computer security)
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.