Cutoff phenomenon for the maximum of a sampling of Ornstein-Uhlenbeck processes

In this article we study the so-called cutoff phenomenon in the total variation distance when n→∞ for the maximum of n ergodic Ornstein–Uhlenbeck processes driven by stable noise of index α. Using the asymptotic theory of extremes; in the Gaussian case we prove that the total variation distance between the distribution of the maximum and its limiting distribution converges to a universal function in a constant time window around the cutoff time, a fact known as profile cutoff in the context of stochastic processes. On the other hand, in the heavy-tailed case we prove that there is not cutoff. ©2020 Elsevier B.V. All rights reserved.