Ocean structures, including ships, boats, piers, docks, rigs and platforms, are subject to fair weather wind and waves, as well as violent storms. A scientific analysis of these structures, under varying conditions, requires a mix of civil engineering, physics and applied mathematics. Chapters by experts in these fields are presented which explore the nonlinear responses of ocean structures to stochastic forcing. Theoretical methods calculate aspects of time, frequency and phase space responses. Probabilities governed by stochastic differential equations are investigated directly or through moment correlations, such as power spectra. Calculations can also involve level crossing statistics and first passage times. This book will help scientists study stochastic nonlinear equations and help engineers design for short term survivability of structures in storms and long life in the face of everyday fatigue.