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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).

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