Excited Brownian Motions

Olivier Raimond (1, 2) , Bruno Schapira (1)

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

We introduce and study a natural continuous time version of excited random walks. In the case of nonnegative drift, we obtain a necessary and sufficient condition for recurrence. This result is analogous to Zerner's result \cite{Zer1} for excited (or cookie) random walks. We use similar arguments.

Mots clés: Reinforced process; Excited process; Self-interacting process

Domaines: Probabilités [math.PR]

Olivier Raimond, Bruno Schapira. Excited Brownian Motions. 2008. ⟨hal-00332059v2⟩