Excited Brownian Motions

Olivier Raimond (1) , Bruno Schapira (2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We study a natural continuous time version of excited random walks, introduced by Norris, Rogers and Williams about twenty years ago. We obtain a necessary and sufficient condition for recurrence and for positive speed. This is analogous to results for excited (or cookie) random walks.

Mots clés: Reinforced process; Excited process; Self-interacting process; Recurrence; Law of large numbers.; Law of large numbers

Domaines: Probabilités [math.PR]

Olivier Raimond, Bruno Schapira. Excited Brownian Motions. 2010. ⟨hal-00332059v4⟩