We analyze the problem of parametric roll in random seas, where the random wave excitation is modeled by anon-white stationary stochastic process. This process is derived from a spectral description of the random seaway using a traveling effective wave. The method of stochastic averaging is applied, such that the fast oscillatory dynamics of roll is averaged over the roll period. This procedure yields equations for the drift and diffusion of the roll energy. With these equations the non-stationary probability density of roll energy is obtained by solving the corresponding Fokker-Planck equation using a finite difference approach. The results can be used to improve ship hull design as well as for controller design to encounter the occurrence of parametric roll resonance.
