Local Markovian property of Gaussian stationary processes

A special class of Gaussian stationary processes which have $k$ derivatives is considered. We assume that the covariance function of the process behaves at the origin so as the covariance function of a process with rational spectral density. It is proved that $(k+1)$-dimensional process (i. е., the process itself and $k$ its derivatives) may be assumed to be Markovian when calculating the asymptotics of functions which are the subintegral expressions in the formula for factorial moments of the number of zero-crossings by tbe process in a small time interval.