English

Exponential functionals of Markov additive processes

Probability 2020-03-06 v2

Abstract

We provide necessary and sufficient conditions for convergence of exponential integrals of Markov additive processes. Other than in the classical L\'evy 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.

Keywords

Cite

@article{arxiv.1911.03168,
  title  = {Exponential functionals of Markov additive processes},
  author = {Anita Behme and Apostolos Sideris},
  journal= {arXiv preprint arXiv:1911.03168},
  year   = {2020}
}
R2 v1 2026-06-23T12:09:07.265Z