Is there a rigorous sense in terms of which a stochastic process may be considered as an approximation to a chaotic but deterministic ODE in a higher-dimensional state space, in a manner that significant theorems asbout the approximability exist?

In which sense is the approximateness rigorously quantitfied?

Is there a rigorous sense in terms of which a stochastic process may be considered as an approximation to a chaotic but deterministic ODE in a higher-dimensional state space, in a manner that significant theorems about the approximability exist?

In which sense is the approximateness rigorously quantitfied?