Bochner-almost periodicity for stochastic processes
Résumé
We compare several notions of almost periodicity for continuous processes defined on the time interval $I=R$ or $I=[0,+\infty)$ with values in a separable Banach space $E$ (or more generally a separable completely regular topological space): almost periodicity in distribution, in probability, in quadratic mean, almost sure almost periodicity, almost sure equi-almost periodicity. In the deterministic case, all these notions reduce to Bochner-almost periodicity, which is equivalent to Bohr-almost periodicity when $I=R$, and to asymptotic Bohr-almost periodicity when $I=[0,+\infty)$.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)