Asymptotic regimes for the occupancy scheme of multiplicative cascades. (English) Zbl 1148.60013

Bertoin, Jean

Stochastic Processes Appl. 118, No. 9, 1586-1605 (2008).

Summary: In the classical occupancy scheme, one considers a fixed discrete probability measure \(\mathbf p = (p_1 : i \in \mathcal I)\) and throws balls independently at random in boxes labeled by \(\mathcal I\), 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 \((\mathbf p(k) : k \in \mathbb N)\) of random probability measures which arise from some multiplicative cascade. Our motivation comes from the study of the asymptotic behavior of certain fragmentation chains.

MSC:

60F15	Strong limit theorems
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

occupancy scheme; multiplicative cascade; asymptotic regime; homogeneous fragmentation

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