Generalized refracted Lévy process and its application to exit problem

Kei Noba and Kouji Yano

Stochastic Processes and their Applications, 2019, vol. 129, issue 5, 1697-1725

Abstract: Generalizing Kyprianou–Loeffen’s refracted Lévy processes, we define a new refracted Lévy process which is a Markov process whose positive and negative motions are Lévy processes different from each other. To construct it we utilize the excursion theory. We study its exit problem and the potential measures of the killed processes. We also discuss approximation problem.

Date: 2019
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DOI: 10.1016/j.spa.2018.06.004

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