On the statistical properties of a stationary process sampled by a stationary point process

Abstract

Let X = { X t } t ∈ T , where T = R or Z , be a strictly stationary process, which is assumed to be strongly mixing. In this paper, we are concerned with the stationarity and the mixing properties of the process obtained from X by a random sampling, that is, { X t n } n ∈ Z , where { t n } n ∈ Z is a real point process. This study is done for ϕ , β , ρ and α -mixing processes.