Abstract
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We present two flexible stochastic models for 2D and 3D ocean waves with potential to reproduce severe and non-homogeneous sea conditions. The first family consists of generalized Lagrange models for the movements of individual water particles. These models can generate crest-trough and front-back statistically asymmetric waves, with the same degree of asymmetry as measured ocean waves. They are still in the Gaussian family and it is possible to calculate different slope distributions exactly from a wave energy spectrum. The second model is a random field model that is generated by a system of nested stochastic partial differential equations. This model can be adapted to spatially non-homogeneous sea conditions and it can approximate standard wave spectra. One advantage with this model is that Hilbert space approximations can be used to obtain computationally efficient representations with Markov-type properties that facilitate the use of sparse matrix techniques in simulation and estimation.