Willing to take criticism on this method of doing it-- you could probably get close by taking advantage of the generic definition of remake in DiffEqBase, but AFAIK you'd have to remove the defined constructor for NoiseProcess and expose the original constructor, which could break a lot of downstream stuff for a tiny tweak. I felt more comfortable adding a few specific, but extensible utilities prescribed for the NoiseProcess type. If you disagree or find this dubious, feel free to close without merging.

Also, I'd be happy to add a test if you're content with the implementation and would like me to.

I think I would test that copy works as intended (same data, different memory)

This is fine, just needs tests.

Xoshiro is only defined v1.7 and above I think, so the test needs a v1.6 version

What is the status of this?

Notice that copy for every type of noise has been recently implemented in #127 and can be useful.

Question? Is remake assume to keep the same field types and just change the values or does it (in general) allow changing the type as well?

Question? Is remake assume to keep the same field types and just change the values or does it (in general) allow changing the type as well?

Nevermind. I just checked that remake for an ODEProblem allows changing the type of fields. But the implemented copy, and any sound implementation of similar keeps the type. So, if we want to allow changing the type, we would need to implement remake directly.