N. E. Kordzakhia, A. A. Novikov, “On maximal inequalities for Ornstein–Uhlenbeck processes with jumps”, Teor. Veroyatnost. i Primenen., 2021, Volume 66, Issue 4,Pages <nobr>895

On maximal inequalities for Ornstein–Uhlenbeck processes with jumps

N. E. Kordzakhia^a, A. A. Novikov^bc

^a Department of Mathematics and Statistics, Macquarie University, Sydney, Australia
^b University of Technology Sydney, Sydney, Australia
^c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We derive moment and exponential inequalities for the maximum of a generalized Ornstein–Uhlenbeck process under some assumptions on tail distributions of a jump component.

Keywords: generalized Ornstein–Uhlenbeck processes, maximal inequality, the Graversen–Peskir inequality, the Legendre transformation.

Received: 05.06.2021
Accepted: 06.07.2021

DOI: 10.4213/tvp5516