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Kac–Lévy Processes

  • Nikita RatanovEmail author
Article
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Abstract

Markov-modulated Lévy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit expressions for the Lévy–Khintchine exponent in the case of a two-state underlying Markov chain. For the renewal case, the limit distributions (as \(t\rightarrow \infty \)) are obtained. In the case of processes with jumps, we present some results for the exponential functional.

Keywords

Markov-modulated Lévy process Markov-switching model Goldstein–Kac process Lévy–Khintchine exponent Lévy–Laplace exponent Mixture of distributions Exponential functional 

Mathematical Subject Classification (2010)

60K15 60J75 60J27 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Facultad de EconomíaUniversidad del RosarioBogotáColombia

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