Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

On processes with conditional independent increments and stable convergence in law

Auteur(s):

Code(s) de Classification MSC:

Résumé: In this paper we study the semiamrtingales $X$ which are defined on an extension of a basic filtered probability space $\Ba=(\Om,\Fa,\fit_{t\geq0},P)$ and which, conditionally on $\Fa$, have independent increments. We first give a general characterization for such processes. Then we prove that if all martingales of the basis $\Ba$ can be written as a sum of stochastic integrals w.r.t. the continuous martingale part and the compensated jump measure of $Y$, then a process $X$ has $\Fa$-conditional independent increments if and only if the characteristics of the pair $(X,Y)$, on the extended space, are indeed predictable w.r.t. the filtration $\fit$. Finally we prove a functional convergence result toward a process $X$ of this kind.

Mots Clés: Stable convergence ; Lévy processes

Date: 2001-05-21

Prépublication numéro: PMA-662