Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes

In this paper, we study the cut-off phenomenon under the total variation distance
of d-dimensional Ornstein-Uhlenbeck processes which are driven by Lévy processes.
That is to say, under the total variation distance, there is an abrupt convergence of
the aforementioned process to its equilibrium, i.e. limiting distribution. Despite that
the limiting distribution is not explicit, its distributional properties allow us to deduce that a profile function always exists in the reversible cases and it may exist in the non-reversible cases under suitable conditions on the limiting distribution. The cut-off phenomena for the average and superposition processes are also determined.