Parametric inference for multidimensional hypoelliptic erfodic diffusion with full observations

Abstract : Multidimensional hypoelliptic diffusions arise naturally as models of neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. We build a consistent estimator of the drift and variance parameters with the help of a discretized log-likelihood of the continuous process when discrete time observations of both coordinates are available on an interval $T = N\Delta$, with $\Delta$ the time step between the observations. We discuss the difficulties generated by the hypoellipticity and provide a proof of the consistency and the asymptotic normality of the estimator in the asymptotic setting $T\to\infty$ as $\Delta\to 0$. We test our approach numerically on the hypoelliptic FitzHugh-Nagumo model, which describes the firing mechanism of a neuron.
Type de document :
Pré-publication, Document de travail
2019
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https://hal.archives-ouvertes.fr/hal-01704010
Contributeur : Anna Melnykova <>
Soumis le : vendredi 11 janvier 2019 - 17:59:21
Dernière modification le : dimanche 27 janvier 2019 - 17:48:31

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  • HAL Id : hal-01704010, version 2
  • ARXIV : 1802.02943

Citation

Anna Melnykova. Parametric inference for multidimensional hypoelliptic erfodic diffusion with full observations. 2019. 〈hal-01704010v2〉

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