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Parametric inference for multidimensional hypoelliptic diffusion with full observations

Authors
  • Melnykova, Anna
Publication Date
Feb 08, 2018
Source
Kaleidoscope Open Archive
Keywords
Language
English
License
Unknown
External links

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 in the case of fully observed data. We discuss the difficulties generated by the hypoellipticity and provide a proof of the consistency of the estimator. We test our approach numerically on the hypoelliptic FitzHugh-Nagumo model, which describes the firing mechanism of a neuron.

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