On exit times of Levy-driven Ornstein-Uhlenbeck processes
Konstantin Borovkov, Alexander Novikov
STATISTICS & PROBABILITY LETTERS | ELSEVIER SCIENCE BV | Published : 2008
We prove two martingale identities which involve exit times of Levy-driven Ornstein-Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transform of the exit time under the assumption that positive jumps of the Levy process are exponentially distributed. © 2008 Elsevier B.V. All rights reserved.
The authors are thankful to G. Miteteli and a referee for their constructive comments. The first author was supported by ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS). The second author was supported by ARC Discovery grant.