Statistical analysis of linear dynamic systems driven by the binary Markovian noise on the basis of the kinetic equations for non-Markovian stochastic processes

A new set of kinetic equations for non-Markovian processes is applied to the statistical description of linear dynamic systems. The expressions for multidimensional kinetic coefficients are presented. As a particular case, the binary Markovian input noise is considered. The problem of the output probability density function definition is solved for a first-order linear dynamic system. Then, the second-order linear filters are investigated. Two-dimensional kinetic equation solutions for the output probability density functions are obtained by a numerical method in the steady-state case.