I'm not sure what a pre-Brownian motion is-- my guess is that it is another name for white noise. If you want a notion of local time of white noise, my guess is that you would take some sort of formal derivative of local time for Brownian motion and then perhaps move the derivative over using some notion of integration by parts. This is vague, but then again, the question was a bit vague.

For both Brownian motion and fractional Brownian motion one space in which you can do these sorts of things is the Hida distribution space. This space is an extension of the typical L2 space in which the Wiener chaos lives (along the lines of the Nualart Vives paper you are citing). In short, typical L2 random variables have chaos decompositions, but this notion can be extended to random distributions (called Hida distributions) which is the dual of an appropriate test function space. The best reference I can think of for this is the SPDE book by Holden, Oksendal, Uboe, and Zhang. In particular, one can take a formal derivative of Brownian motion and show that is lives in this space (for example see the paper of elliot and van der Hoek in 2003).