On an application of the Guillouzic's scheme for a calculation of the matrix of spectral densities for the state vector of a linear delay differential stochastic system

In the paper, the Guillouzic's scheme suggested for a calculation of the stationary probability density function of solution for a linear stochastic delay differential equation of the first degree with constant coefficients is applied for an analysis of steady-state oscillations in a linear stochastic system which is perturbed by stationary noise being differentiable in the mean square sense. The aim of the study is to construct the matrix of spectral densities for the state vector of the system. It is supposed that analytical results will be used for calculations of motion characteristics of different types of vehicles traveling at a constant speed on rough roads with random microprofiles.