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# Parametric inference for multidimensional hypoelliptic ergodic diffusion with full observations

2 SVH - Statistique pour le Vivant et l’Homme
LJK - Laboratoire Jean Kuntzmann
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.
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Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-01704010
Contributor : Anna Melnykova Connect in order to contact the contributor
Submitted on : Friday, January 11, 2019 - 5:59:21 PM
Last modification on : Tuesday, October 19, 2021 - 11:26:47 AM

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### Identifiers

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

### Citation

Anna Melnykova. Parametric inference for multidimensional hypoelliptic ergodic diffusion with full observations. 2019. ⟨hal-01704010v2⟩

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