Many wave energy converter (WEC) designs emerging over the recent years are floating cylindrical geometries with position-keeping mooring system. However, the dynamic stability of these novel floating structures under random sea states has not been investigated adequately. The Melnikov function model and the Markov process model are two efficient approaches providing quantitative predictions of capsizing. In this study, application of the two methods to a moored floating cylinder representing a generic WEC, has been explored to predict the risks of pitchpoling under random excitation. Using the Melnikov approach, the rate of phase space flux was evaluated to quantify the dynamic stability. This approach is compared with the Markov approach, which evaluates the mean first escape (capsize) rate to quantify the dynamic stability. The two methods are investigated through studies using various parameters. The similarity of their results and the differences of their approximations will be explored.