ABSTRACT
Indeed, if y(t) is a stationary narrow-band Gaussian process with a nonzero mean frequency, obtained by passing a white noise through a linear shaping filter, the latter should be at least of second order. There is a certain case, however, that is amenable to a complete analytical solution for an arbitrary relation between bandwidths of the system and of the excitation spectrum. This is the case of a sinusoidal y(t) with a white noise phase modulation (PM). It may be added that the case of the periodic parametric excitation with a white noise PM is not only of purely academic interest. A clear example from mechanics, which is important for various applications, is that of a straight pipe with a slug flow of a two-phase fluid with periodically alternating slugs of, say, steam and water. In other words, any sufficiently small white-noise variations of the parametric excitation frequency are always stabilizing in probability.
