Open Access
2020 Exponential functionals of Markov additive processes
Anita Behme, Apostolos Sideris
Electron. J. Probab. 25: 1-25 (2020). DOI: 10.1214/20-EJP441


We provide necessary and sufficient conditions for convergence of exponential integrals of Markov additive processes. By contrast with the classical Lévy case studied by Erickson and Maller we have to distinguish between almost sure convergence and convergence in probability. Our proofs rely on recent results on perpetuities in a Markovian environment by Alsmeyer and Buckmann.


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Anita Behme. Apostolos Sideris. "Exponential functionals of Markov additive processes." Electron. J. Probab. 25 1 - 25, 2020.


Received: 3 September 2019; Accepted: 4 March 2020; Published: 2020
First available in Project Euclid: 27 March 2020

zbMATH: 07206374
MathSciNet: MR4089787
Digital Object Identifier: 10.1214/20-EJP441

Primary: 60H10 , 60J75
Secondary: 60G51 , 60J25

Keywords: exponential functional , Lévy process , Markov additive process , Markov modulated perpetuity , Markov switching model

Vol.25 • 2020
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