We define a local time flow of skew Brownian motions ,that is, a
family of solutions to the stochastic differential equation defining the skew
Brownian motion, starting from different points but driven by the same Brownian
motion. We prove several results on distributional and path properties of the
flow. Our main result is a version of the Ray–Knight theorem on local
times. In our case, however, the local time process viewed as a function of the
spatial variable is a pure jump Markov process rather than a diffusion.