Comparison of some approaches to stability of a sdof system under random parametric excitation

We give a rigorous comparison of the asymptotic stochastic averaging method and the moment Lyapunov exponent approach in assessing the mean-square stability through an example of a single-degree-of-freedom system under small periodic parametric excitation with random phase modulation. The comparison is based on an efficient numerical procedure to determine the regions of mean-square stability.