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Is a Brownian Motion Skew?

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Listed:
  • Antoine Lejay
  • Ernesto Mordecki
  • Soledad Torres

Abstract

type="main" xml:id="sjos12033-abs-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.

Suggested Citation

  • Antoine Lejay & Ernesto Mordecki & Soledad Torres, 2014. "Is a Brownian Motion Skew?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 346-364, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:346-364
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    File URL: http://hdl.handle.net/10.1111/sjos.12033
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    References listed on IDEAS

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    1. Olivier Bardou & Miguel Martinez, 2010. "Statistical estimation for reflected skew processes," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 231-248, October.
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    Cited by:

    1. Song, Shiyu & Wang, Suxin & Wang, Yongjin, 2016. "On some properties of reflected skew Brownian motions and applications to dispersion in heterogeneous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 90-105.

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