Accéder directement au contenu Accéder directement à la navigation

Hypoelliptic diffusions: discretization, filtering and inference from complete and partial observations

Abstract : The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates of the multi-dimensional process operate on different time scales, standard inference tools are ill conditioned. In this paper, we propose to use a higher order scheme to discretize the process and approximate the likelihood, such that the different time scales are appropriately accounted for. We show consistency and asymptotic normality with non-typical convergence rates. When only partial observations are available, we embed the approximation into a filtering algorithm for the unobserved coordinates, and use this as a building block in a Stochastic Approximation Expectation Maximization algorithm. We illustrate on simulated data from three models; the Harmonic Oscillator, the FitzHugh-Nagumo model used to model the membrane potential evolution in neuroscience, and the Synaptic Inhibition and Excitation model used for determination of neuronal synaptic input.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

Littérature citée [38 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01627616
Contributeur : Adeline Samson <>
Soumis le : jeudi 2 novembre 2017 - 10:23:25
Dernière modification le : jeudi 26 mars 2020 - 20:49:58
Document(s) archivé(s) le : samedi 3 février 2018 - 13:16:42

Fichier

hypoSDE_arxiv.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01627616, version 1

Collections

Citation

Susanne Ditlevsen, Adeline Samson. Hypoelliptic diffusions: discretization, filtering and inference from complete and partial observations. 2017. ⟨hal-01627616v1⟩

Partager

Métriques

Consultations de la notice

293

Téléchargements de fichiers

75