  We study the non-Markovian random continuous processes described by the
Mori-Zwanzig equation. As a starting point, we use the Markovian Gaussian
Ornstein-Uhlenbeck process and introduce an integral memory term depending on
the past of the process into expression for the higher-order transition
probability function and stochastic differential equation. We show that the
proposed processes can be considered as continuous-time interpolations of
discrete-time higher-order autoregressive sequences. An equation connecting the
memory function (the kernel of integral term) and the two-point correlation
function is obtained. A condition for stationarity of the process is
established. We suggest a method to generate stationary continuous stochastic
processes with prescribed pair correlation function. As illustration, some
examples of numerical simulation of the processes with non-local memory are
presented.
