Comptes Rendus
no. 5
Statistics
On likelihood estimation for a discretely observed jump process
[Sur l'estimation d'un processus de sauts discretisé]

Présenté par : Paul Deheuvels

Dominique Dehay1 ; Jian-feng Yao1
1 IRMAR, campus de Beaulieu, 35042 Rennes cedex, France
Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 341-344.

Soit un processus de sauts markovien observé en des temps discrets. À l'aide d'une formule explicite de la vraisemblance de la chaîne observée, nous proposons une théorie asymptotique de l'estimateur de vraisemblance.

We consider the parameter estimation problem for a Markov jump process sampled at periodic epochs with a constant step. Unlike the diffusion case where a closed form of the likelihood function is usually unavailable, we provide here an explicit expression of the likelihood function of the sampled chain. Moreover under suitable ergodicity condition on the jump process, we establish the consistency and the asymptotic normality of the likelihood estimator as the observation period tends to infinity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.12.025

Dominique Dehay 1 ; Jian-feng Yao 1

1 IRMAR, campus de Beaulieu, 35042 Rennes cedex, France 
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Dominique Dehay; Jian-feng Yao. On likelihood estimation for a discretely observed jump process. Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 341-344. doi : 10.1016/j.crma.2005.12.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.025/

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