Stochastic model construction of observed random phenomena

• A stochastic model for non-Gaussian and nonstationary random phenomena is proposed.
• No a priori assumptions are introduced in the model.
• The model probability distribution is derived explicitly.
• The model is applied for the construction of seismic acceleration models.

A method for constructing probabilistic models of non-stationary time dependent natural hazards is proposed. It is based on the use of Karhunen–Loève expansion and of a kernel estimator for the distribution of the multivariate random variables appearing in the expansion. The terms of the expansion and the distribution are identified from available measures. The approach is assessed through an academic example and is then applied to seismic ground motion modelling based on recorded data.