Penalizing a $BES(d)$ process (0 < d < 2) with a function of its local time, V

Bernard Roynette (1, 2) , Pierre P. Vallois (1, 2) , Marc Yor (3)

1 IECN - Institut Élie Cartan de Nancy
2 TOSCA - Simuler et calibrer des modèles stochastiques
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We describe the limit laws, as $t \rightarrow \infty$ , of a Bessel process $(Rs_s, s\leq t)$ of dimension $d \in(0, 2)$ penalized by an integrable function of its local time $L_t$ at 0, thus extending our previous work of this kind, relative to Brownian motion.

Mots clés: Penalization; Bessel process; Local time

Domaines: Probabilités [math.PR]

Bernard Roynette, Pierre P. Vallois, Marc Yor. Penalizing a $BES(d)$ process (0 < d < 2) with a function of its local time, V. Studia Scientiarum Mathematicarum Hungarica, 2008, 45 (1), pp.67-124. ⟨10.1556/sscmath.2007.1042⟩. ⟨hal-00141533⟩