The Self-Similar Dynamics of Renewal Processes - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Electronic Journal of Probability Année : 2011

The Self-Similar Dynamics of Renewal Processes

Marina Talet
  • Fonction : Auteur
  • PersonId : 978028
Albert Meads Fisher
  • Fonction : Auteur
  • PersonId : 978029

Résumé

We prove an almost sure invariance principle in log density for renewal processes with gaps in the domain of attraction of an α -stable law. There are three different types of behavior: attraction to a Mittag-Leffler process for 0<α<1, to a centered Cauchy process for α=1 and to a stable process for 1<α≤2 . Equivalently, in dynamical terms, almost every renewal path is, upon centering and up to a regularly varying coordinate change of order one, and after removing a set of times of Cesàro density zero, in the stable manifold of a self-similar path for the scaling flow. As a corollary we have pathwise functional and central limit theorems.

Dates et versions

hal-01285495 , version 1 (09-03-2016)

Identifiants

Citer

Marina Talet, Albert Meads Fisher. The Self-Similar Dynamics of Renewal Processes. Electronic Journal of Probability, 2011, 16 (31), pp.33. ⟨10.1214/EJP.v16-888⟩. ⟨hal-01285495⟩
50 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More