Is a Brownian skew?
Probability
2015-03-17 v1 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1101.0933,
title = {Is a Brownian skew?},
author = {Antoine Lejay and Ernesto Mordecki and Soledad Torres},
journal= {arXiv preprint arXiv:1101.0933},
year = {2015}
}
Comments
26 pages, 8 figures