Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion

Antoine Lejay 1, 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We study the asymptotic property of simple estimator of the parameter of a Skew Brownian Motion when one observes its positions on a fixed grid — or equivalently of a simple random walk with a bias at 0. This estimator, nothing more than the Maximum Likelihood Estimator, is based only on the number of passages of the random walk at 0. It is very simple to set up, is consistent and is asymptotically mixed normal. We believe that this simplified framework is helpful to understand the asymptotic behavior of the maximum likelihood of the Skew Brownian Motion observed at discrete times which is studied in a companion paper.
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https://hal.inria.fr/hal-01319319
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Submitted on : Friday, May 12, 2017 - 4:29:00 PM
Last modification on : Saturday, October 6, 2018 - 1:16:22 AM

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Antoine Lejay. Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion. Statistical Inference for Stochastic Processes, Springer Verlag, 2018, 21 (3), pp.539-551. ⟨10.1007/s11203-017-9161-9⟩. ⟨hal-01319319v4⟩

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