**Approximation of stationary random functions with fractional
rational spectral density
**

The paper deals with the approximation of stationary random functions with a prescribed fractional rational spectral density. The approximations are found from stationary solutions of so-called form filter equations which are ODEs with an inhomogeneous term containing a given random function. Here, this random function is weakly correlated and ideas of form filter theory are combined with expansions of spectral densities of stationary solutions with respect to the correlation length. Further, the smoothing of derivatives of the approximated functions is considered. Some examples concerning modeling of random road and railway profiles are given.