On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein-Uhlenbeck processes. (English) Zbl 07879395
Summary: We establish sufficient conditions for the existence, and derive explicit formulas for the \(\kappa\)’th moments, \(\kappa\geq 1\), 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.
Our derivations rely on new general results on moments of Markov additive processes and (multidimensional) integrals with respect to Markov additive processes.
MSC:
| 60G10 | Stationary stochastic processes |
| 60G51 | Processes with independent increments; Lévy processes |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J27 | Continuous-time Markov processes on discrete state spaces |
Keywords:
exponential functional; generalized Ornstein-Uhlenbeck process; Lévy process; Markov additive process; Markov switching model; moments; stationary processReferences:
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