On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein–Uhlenbeck processes

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

We establish sufficient conditions for the existence, and derive explicit formulas for the κ’th moments, κ≥1, of Markov modulated generalized Ornstein–Uhlenbeck processes as well as their stationary distributions. In particular, the running mean, the autocovariance function, and integer moments of the stationary distribution are derived in terms of the characteristics of the driving Markov additive process. Our derivations rely on new general results on moments of Markov additive processes and (multidimensional) integrals with respect to Markov additive processes.

Details

Original languageEnglish
Article number104382
JournalStochastic processes and their applications
Volume174
Publication statusPublished - Aug 2024
Peer-reviewedYes

External IDs

Scopus 85192854350
Mendeley 9bf0e8c4-c4c9-36f6-88ae-bcdb35827bab

Keywords

Keywords

  • Markov additive process, Generalized Ornstein–Uhlenbeck process, Lévy process, Moments, Stationary process, Markov switching model, Exponential functional

Library keywords