On the existence of a periodic model for a class of stochastic processes

The existence of a periodic solution to a class of nonlinear Riccati equations is considered. A set of conditions to be satisfied by the coefficients of the Riccati equation and proper initial condition leads to the periodic solution. This class of equations appears in the solution to the factorization problem; i.e., determination of a linear system which transforms white noise into a possibly nonstationary random process with a specified covariance function.