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

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  • Behme, Anita
  • Di Tella, Paolo
  • Sideris, Apostolos

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.

Suggested Citation

  • Behme, Anita & Di Tella, Paolo & Sideris, Apostolos, 2024. "On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:spapps:v:174:y:2024:i:c:s0304414924000887
    DOI: 10.1016/j.spa.2024.104382
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    References listed on IDEAS

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    1. Zhang, Lidong & Jiang, Chunmei, 2009. "Stationary distribution of reflected O-U process with two-sided barriers," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 177-181, January.
    2. Kevei, Péter, 2018. "Ergodic properties of generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 156-181.
    3. Lindner, Alexander & Maller, Ross, 2005. "Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1701-1722, October.
    4. Søren Asmussen & Mogens Bladt, 2022. "Gram–Charlier methods, regime-switching and stochastic volatility in exponential Lévy models," Quantitative Finance, Taylor & Francis Journals, vol. 22(4), pages 675-689, April.
    5. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    6. P. Salminen & L. Vostrikova, 2016. "On exponential functionals of processes with independent increments," Papers 1610.08732, arXiv.org, revised Mar 2018.
    7. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
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