  The purpose of this article is to give another proof on the existence of a
diffusion on a junction, which has been already done by M.Freidlin and
S-J.Sheu, in Diffusion processes on graphs, (2000). We generalize the result to
time dependent and borel coefficients. Such a process can be seen as a couple
(x, i) with x a one dimensional continuous diffusion whose coefficients depends
on the edge i where it is located. We then provide an It{\^o}'s formula for
this process. Finally, we give an estimate of the local time of the process at
the junction point.
