Sharp bounds for the expected occupation density of Itô processes with bounded irregular drift and diffusion coefficients

We find explicit and optimal upper and lower bounds for the expected occupation density for an Itô process when its drift and diffusion coefficients are unknown under boundedness and ellipticity conditions on the coefficients. This is related to the optimal bound for the expected interval occupation found in [2]. In contrast, our bound is for a single point and the resulting formula is less involved. Our findings allow us to find explicit upper and lower bounds for mean path integrals.