Localisable moving average symmetric stable and multistable processes
Résumé
We study a particular class of moving average processes which possess a property called localisability. This means that, at any given point, they admit a “tangent process”, in a suitable sense. We give general conditions on the kernel g defining the moving average which ensures that the process is localisable and we characterize the nature of the associated tangent processes. Examples include the reverse Ornstein-Uhlenbeck process and the multistable reverse Ornstein-Uhlenbeck process. In the latter case, the tangent process is, at each time t, a Lévy stable motion with stability index possibly varying with t. We also consider the problem of path synthesis, for which we give both theoretical results and numerical simulations.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...