Asymptotic regimes for the occupancy scheme of multiplicative cascades

Jean Bertoin (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 DMA - Département de Mathématiques et Applications - ENS Paris

In the classical occupancy scheme, one considers a fixed discrete probability measure ${\bf p}=(p_i: {i\in{\cal I}})$ and throws balls independently at random in boxes labeled by ${\cal I}$, such that $p_i$ is the probability that a given ball falls into the box $i$. In this work, we are interested in asymptotic regimes of this scheme in the situation induced by a refining sequence $({\bf p}(k) : k\in\N)$ of random probability measures which arise from some multiplicative cascade. Our motivation comes from the study of the asymptotic behavior of certain fragmentation chains

Mots clés: homogeneous fragmentation; Occupancy scheme; multiplicative cascade; asymptotic regime; homogeneous fragmentation.

Domaines: Probabilités [math.PR]

Jean Bertoin. Asymptotic regimes for the occupancy scheme of multiplicative cascades. 2007. ⟨hal-00161832v2⟩