The laws of Brownian local time integrals
Résumé
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 ${\tt d}$, $0<{\tt d}<2$.
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