On the local time density of the reflecting Brownian bridge (Q1580050)

The authors generalize a representation of the one-dimensional density of the total local time \(\tau^+(a)\) of the reflecting Brownian bridge at level \(a\) to several dimensions. They offer two different approaches to find an expression for the multidimensional density of \((\tau^+ (\rho_1), \dots, \tau^+ (\rho_d))\): The first one presents a direct computation by means of Kac's formula for Brownian functionals and the second one is indirect and based on the fact that the process consisting of suitably normalized strata of a random mapping converges weakly to Brownian bridge local time.