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We find explicit and optimal upper bounds for the expected occupation densityfor an It\^o-process when its drift and diffusion coefficients are unknownunder boundedness and ellipticity conditions on the coefficients. This isrelated to the optimal bound for the expected interval occupation found inAnkirchner and Wendt(2021). In contrast, our bound is for a single point andthe resulting formula is less involved. Our findings allow us to find explicitupper bounds for mean path integrals.

A sharp upper bound for the expected occupation density of It\^o processes with bounded irregular drift and diffusion coefficients