# SAMOS-MATISSE - CES - UMR 8174

## Rechercher

Sur ce site

Sur le Web du CNRS

Accueil du site > Séminaires > Probabilités Statistiques et réseaux de neurones > Random coefficient AR(1) process with heavy-tailed renewal-switching coefficient and heavy-tailed noise

Vendredi 24 mars 2006 à 12 heures

## Random coefficient AR(1) process with heavy-tailed renewal-switching coefficient and heavy-tailed noise

Donatas SURGAILIS (membre de l’Académie des Sciences de Lituanie)

Abstract : We discuss limit behavior of the partial sums process of stationary solution of AR(1) equation , with random (renewal-reward) coefficient , taking iid\ values on consecutive intervals of a stationary renewal process with heavy-tailed interrenewal distribution, and with iid\ innovations belonging to the domain of attraction of an stable law . Under suitable conditions on the tail parameter of the interrenewal distribution and the singularity parameter of the distribution of near unit root , we show that the partial sums process of converges to a stable Lévy process with index . The paper extends the result of Leipus and Surgailis (2003) from finite variance to infinite variance .

Dans la même rubrique :