Supplementary material

Theorem A.1 (Deterministic scaling limit of stochastic processes) . The reader interested in the proof is referred to the supplementary materials of [21, 31]. Although the theorem wasn't originally proven in the A.1 corresponds to 1 /δt, where δt is defined in Theorem 2.1. Before proving this proposition, we begin with a small lemma: Lemma B.2. We are now in a position to show Theorem B.1: 16 Proof.