It could be, I’m not familiar enough with the class inheritance structure of random variables to understand what is going on at just a glance of the code. Looking at the code here, it seems like the logp and rng_fn functions use centered normals, but I could be looking at the totally wrong place, or not understanding what I am reading. Perhaps @ricardoV94 knows if there is any merit to doing something like I proposed?
(I also looked for a discussion in the stan community about centered vs non-centered GRW, but didn’t come up with anything, for what its worth)
With these caveats, you would add a initial distribution by defining it as you wish, then manually concatenating it to the beginning of mu + sigma * offset, then taking the cumsum of the new vector.
If you want to pool information from the player and period dimensions together, yes I think so.