The almost sure limits of the minimal position and the additive martingale in a branching random walk.

Yueyun Hu (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

Consider a real-valued branching random walk in the boundary case. Using the techniques developed by Aïdékon and Shi [5], we give two integral tests which describe respectively the lower limits for the minimal position and the upper limits for the associated additive martingale.

Mots clés: integral tests; Branching random walk; minimal position; additive martingale; integral tests.

Domaines: Probabilités [math.PR]

Yueyun Hu. The almost sure limits of the minimal position and the additive martingale in a branching random walk.. 2012. ⟨hal-00755972v2⟩