Open Access
2020 Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes
Gerardo Barrera, Juan Carlos Pardo
Electron. J. Probab. 25: 1-33 (2020). DOI: 10.1214/20-EJP417


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.


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Gerardo Barrera. Juan Carlos Pardo. "Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes." Electron. J. Probab. 25 1 - 33, 2020.


Received: 2 January 2020; Accepted: 10 January 2020; Published: 2020
First available in Project Euclid: 5 February 2020

zbMATH: 07206352
MathSciNet: MR4073676
Digital Object Identifier: 10.1214/20-EJP417

Primary: 37A25 , 60E07 , 60G10 , 60G51 , 60G60

Keywords: cut-off phenomenon , Lévy processes , Ornstein-Uhlenbeck processes , total variation distance

Vol.25 • 2020
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