Convergence to stable laws in the space $D$

François Roueff (1) , Philippe Soulier (2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 MODAL'X - Modélisation aléatoire de Paris X

We study the convergence of centered and normalized sums of i.i.d. random elements of the space $\mathcal{D}$ of c{á}dl{á}g functions endowed with Skorohod's $J_1$ topology, to stable distributions in $\mathcal D$. Our results are based on the concept of regular variation on metric spaces and on point process convergence. We provide some applications, in particular to the empirical process of the renewal-reward process.

Mots clés: Regular variation; stable processes; functional convergence.

Mots clés: functional convergence

Domaines: Probabilités [math.PR]

François Roueff, Philippe Soulier. Convergence to stable laws in the space $D$. 2012. ⟨hal-00755255v2⟩