A new probabilistic insight into the structure of local time is presented. A convolution formula for the local time at 0 of Itô diffusions reflecting at 0 is obtained. A simple integro-differential equation for the cumulative distribution function of the local time is given. Finally, a probabilistic representation of a generalized Stroock–Williams equation is presented.
"A convolution formula for the local time of an Itô diffusion reflecting at 0 and a generalized Stroock–Williams equation." Bernoulli 27 (3) 1870 - 1898, August 2021. https://doi.org/10.3150/20-BEJ1295