The maximal drawdown of the Brownian meander

Yueyun Hu (1) , Zhan Shi (2) , Marc Yor (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Motivated by evaluating the limiting distribution of randomly biased random walks on trees, we compute the exact value of a negative moment of the maximal drawdown of the standard Brownian meander.

Mots clés: Brownian meander; Bessel process; maximal drawdown 2010 Mathematics Subject Classification 60J65

Domaines: Probabilités [math.PR]

Yueyun Hu, Zhan Shi, Marc Yor. The maximal drawdown of the Brownian meander. Electronic Communications in Probability, 2015, 20 (39), ⟨10.1214/ECP.v20-3945⟩. ⟨hal-01301802⟩