Properties of the intrinsically stationary stochastic processes

Intrinsically stationary random processes with continuous time are investigated. Their connections with second-order stationary processes and processes with the second-order stationary increments are studied. The properties of semivariogram of the stationary random processes are investigated. Necessary and sufficient conditions for continuity, differentiability and integrability in the mean square sense of the intrinsically stationary stochastic processes in terms of their semivariogram are found. It is shown that the derivative in the mean square sense of the intrinsically stationary random process, for which the second-order moment is exists, is a second-order stationary random process.