In this work, the path integration method and the energy-based stochastic averaging method are introduced in order to study the stochastic responses of ship roll motion in random beam seas. Based on the Markov property of the dynamical system, the path integration (PI) method provides approximate solution to the governing Fokker-Planck (FP) equation. On the other hand, the stochastic averaging method leads to a dimension reduction of the original system, but the essential behavior is retained. Then numerical solution or even analytical solution of the low-dimensional FP equation can be obtained. Since the principles of the above two stochastic methods are different, a comparative study is valuable and noticeable. The accuracy and performance of each method are evaluated with the assistance of Monte Carlo simulation (MCS).
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