Derivation of the spectral density function for solution of linear stochastic partial differential equation with constant delays

This paper is devoted to extension of the scheme of S. Guillouzic, proposed to calculate the spectral density functions for solutions of linear stochastic differential equations of the first order with constant coefficients and one fixed delay, to a new family of equations, i.e. stochastic evolutionary partial differential equations with few constant delays. The aim of our study was to construct the spectral density function of a stationary random field as the solution of hyperbolic equation with fixed coefficients and with random input.