LAUSR

In this paper, we study the cut-off phenomenon of $d$-dimensional Ornstein-Uhlenbeck processes which are driven by Levy processes under the total variation distance. To be more precise, we prove the abrupt convergence under the total variation distance of the aforementioned process to its equilibrium. Despite that the invariant 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. The cut-off phenomenon for the average and superposition processes is also determined.