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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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