Multiple Markov Gaussian processes
Volume 48 / 2021
Applicationes Mathematicae 48 (2021), 65-78
MSC: Primary 60J05; Secondary 37A05.
DOI: 10.4064/am2411-1-2021
Published online: 1 April 2021
Abstract
We get a necessary and sufficient condition on the density of the spectral measure for stationary Gaussian processes with a discrete set of parameters to be Markov of order $k$. We introduce a natural definition of the Markov property of order $r\in \mathbb R_+,$ in the case of continuous parameter. Moreover we give an extension of multiple Markov Gaussian processes with discrete parameters to Gaussian semiflows with some weaker property than the multiple Gaussian property.
