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

Let X={Xt}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, {Xtn}n∈Z, where {tn}n∈Z is a real point process. This study is done for ϕ, β, ρ and α-mixing processes.