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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
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