White noise limits for discrete dynamical systems driven by fast deterministic dynamics

We study a class of singularly perturbed dynamical systems that have fast and slow components, ε⪡1 being the fast to slow timescale ratio. The fast components are governed by a strongly mixing discrete map, which is iterated at time intervals ε. The slow components are governed by a first-order finite-difference equation that uses a time step ε. As ε tends to zero, the fast components may be eliminated, giving rise to SDEs for the slow components. The emerging stochastic calculus is, in the general case, of neither Itô nor Stratonovich type, but depends on the correlation time of the mixing process.