Generalized refracted Lévy process and its application to exit problem

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 m...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 129; no. 5; pp. 1697 - 1725
Main Authors Noba, Kei, Yano, Kouji
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.05.2019
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2018.06.004