Statistiques de diffusions et temps local. (Statistics of diffusions and local times)
type: Item
instance of: scholarly article
title: Statistiques de diffusions et temps local. (Statistics of diffusions and local times)
zbMATH Open document ID: 0636.62084
author: D. Florens-Zmirou
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77320
review text: Consider a real-valued diffusion process the diffusion and drift coefficients of which are respectively a constant number and a function depending on some unknown parameter \(\theta\). Suppose moreover that we do not observe completely the diffusion but only its zero crossing times after excursions longer than some \(\epsilon\). We want to estimate \(\theta\) ; this work provides us with a systematic statistical study of this problem. A quasi-likelihood is introduced and the asymptotic properties of the estimators as the time goes to infinity are proved: consistency, asymptotic normality.
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 4036976
zbMATH Keywords: Lévy measure
zbMATH Keywords: local time
zbMATH Keywords: zero crossing times after excursions
zbMATH Keywords: quasi- likelihood
zbMATH Keywords: consistency
zbMATH Keywords: asymptotic normality
reviewed by: Jean Picard
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4036976