Distribution of functionals of local time of Brownian motion with discontinuous drift

Diffusion with piecewise constant drift and the diffusion coefficient 1 is considered. We call this process the Brownian motion with discontinuous drift. With equal constants this diffusion includes Brownian motion with linear drift, and with opposite sign constants it turns into Brownian motion with alternating drift. We are interested in the result that allows us to calculate the distributions of the integral functionals with respect to the spatial variable of the local time of Brownian motion with discontinuous drift. The explicit form of the distribution of the supremum with respect to spatial variable of the local time of Brownian motion with discontinuous drift is calculated.