Two consistent estimators for the Skew Brownian motion

Abstract : The Skew Brownian motion is of primary importance in modeling diffusion in media with interfaces which arise in many domains ranging from population ecology to geophysics and finance. We show that the maximum likelihood estimator provides a consistent estimator of the parameter of a Skew Brownian motion observed at discrete times. The difficulties are that this process is only null recurrent and has a singular distribution with respect to the one of the Brownian motion. Finally, using the idea of the Expectation-Maximization algorithm, we show that the maximum likelihood estimator can be naturally interpreted as the expected number of positive excursions divided by the expected number of excursions.
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Submitted on : Friday, January 11, 2019 - 12:46:46 PM
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Antoine Lejay, Ernesto Mordecki, Soledad Torres. Two consistent estimators for the Skew Brownian motion. ESAIM: Probability and Statistics, EDP Sciences, In press. ⟨hal-01492853v5⟩

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