First passage times of subordinators and urns

Philippe Marchal (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

It is well-known that the first time a stable subordinator reaches [1, +∞). is Mittag-Leffler distributed. These distributions also appear as limiting distributions in triangular Polya urns. We give a direct link between these two results, using a previous construction of the range of stable subordinators. Beyond the stable case, we show that for a subclass of complete subordinators in the domain of attraction of stable subordinators, the law of the first passage time is given by the limit of an urn with the same replacement rule but with a random initial composition.

Mots clés: stable subordinator; first passage time; Polya urn

Domaines: Probabilités [math.PR]

Philippe Marchal. First passage times of subordinators and urns. A lifetime of excursions through random walks and Lévy processes, 2021. ⟨hal-03063774⟩