Martingales and Rates of Presence in Homogeneous Fragmentations
Résumé
In mass-conservative homogeneous fragmentations, sizes of the fragments decrease at {\bf asymptotic} exponential rates. Like in branching processes, two situations occur: either the number of such fragments is exponentially growing - the rate is effective -, or the probability of presence of such fragments is exponentially decreasing. In a recent paper, N. Krell considers fragments whose sizes decrease at {\bf exact} exponential rates. In this new setting, she characterizes the effective rates and studies Hausdorff dimension. The present paper carries out a detailed analysis of this model and focus on presence probabilities, using the spine method and a suitable martingale. For the sake of completeness, we compare our results with results and methods of the classical model.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)