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The laws of Brownian local time integrals. (English) Zbl 1123.60065
Summary: We obtain some identities in law and some limit theorems for integrals of the type $$\int^t_0\varphi(s)\,dL_s$$. Here $$\varphi$$ is a positive locally bounded Borel function and $$L_t$$ denotes the local time at 0 of processes such as Brownian motion, Brownian bridge, Ornstein-Uhlenbeck process, Bessel process or Bessel bridge of dimension $$d$$, $$0<d<2$$.
##### MSC:
 60J55 Local time and additive functionals 60J65 Brownian motion 60F05 Central limit and other weak theorems
##### Keywords:
Laplace transforms; explicit laws; limit theorems