We present a "Tanaka-like" representation for $\alpha(x, B)$, the local time of intersection for Brownian motion in 2 and 3 dimensions, where $\alpha(x, B)$ is formally $\int_B \int \delta_x(\omega_t - \omega_s) ds dt$.
"A Representation for the Intersection Local Time of Brownian Motion in Space." Ann. Probab. 13 (1) 145 - 153, February, 1985. https://doi.org/10.1214/aop/1176993072