The laws of Brownian local time integrals

Mihai Gradinaru (1) , Bernard Roynette (1) , Pierre Vallois (1) , Marc Yor (2)

1 IECN - Institut Élie Cartan de Nancy
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$ denotes the local time at 0 of processes such as Brownian motion, Brownian bridge, Ornstein-Uhlenbeck process, Bessel process or Bessel bridge of dimension ${\tt d}$, $0<{\tt d}<2$.

Mots clés: Brownian local time

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Mihai Gradinaru, Bernard Roynette, Pierre Vallois, Marc Yor. The laws of Brownian local time integrals. Computational & Applied Mathematics, 1999, 18, pp.259-331. ⟨hal-00091335⟩