Abstract:
A skew Brownian motion with piecewise constant drift is considered. With equal constants this diffusion includes a skew Brownian motion with linear drift and with opposite sign constants it turns into a skew Brownian motion with alternating drift. We are interested in a result that allows us to calculate the distributions of the integral functionals with respect to the spatial variable of the local time of a skew Brownian motion with discontinuous drift.
Key words and phrases:Brownian motion with discontinuous drift, skew Brownian motion, local time.