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

Anita Behme, Paolo Di Tella and Apostolos Sideris

Stochastic Processes and their Applications, 2024, vol. 174, issue C

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.

Keywords: Exponential functional; Generalized Ornstein–Uhlenbeck process; Lévy process; Markov additive process; Markov switching model; Moments; Stationary process (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104382

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