On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein–Uhlenbeck processes
Research output: Contribution to journal › Research article › Contributed › peer-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 language | English |
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Article number | 104382 |
Journal | Stochastic processes and their applications |
Volume | 174 |
Publication status | Published - Aug 2024 |
Peer-reviewed | Yes |
External IDs
Scopus | 85192854350 |
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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