RNG in DiscreteProblem solver

Hi everyone, I have a DiscreteProblem that uses a random number generator, and I’d like to make it reproducible. In the solver for SDEProblems, I can specify a seed (if not an RNG) - do I need to compose a new init/step! method to maintain a specific RNG?

Is this supposed to be a state space problem?

It’s basically this model (see code at end)

Isn’t that the same as what’s handled in DifferenceEquations?