White Noise Space and Local Time This question follows from the answer I gave to the question "Wiener Meets Sobolev" in the MathStackExchange Forum. 
I was wondering in the context of White Noise Space if the Local Time at x of a pre-Brownian motion is a notion that can be properly defined.
Best regards
PS: 
I posted this very same question on MathSE but didn't received any answer, so I allow myself to post it here (as advised by a MathSE Forum member). 
 A: 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).
A: Hi this post is unfortunately not to answer the question which is still open on my side but rather to try to extend it to a more general case. 
Here it is,
We are given $S$ a continuous Semi-martingale. As it is (uniquely) decomposable into a continuous local martingale process $M$ and a continuous Finite Variation process $F$ (theorem 1), it is a special semi-martingale, and its decomposition into a continuous local martingale process and a compensator process (i.e. a continuous FV process) is given by $M$ and $F$. 
I am interested in the way I can define explicitely such processes ($S,M,F$) through the White Noise Space Analysis. 
Both references or direct answers are ok 
Best regards
