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This paper aims to present an approach for the probabilistic characterization of the response of linear structural systems subjected to random time-dependent non-Gaussian actions.

Its fundamental property is working directly on the probability density functions of the actions and responses. This avoids passing through the evaluation of the response statistical moments or cumulants, reducing the computational effort in a consistent measure.

It is an efficient method, for both its computational effort and its accuracy, above all when the input and output processes are strongly non-Gaussian.

This approach can be considered as a dynamic generalization of the probability transformation method recently used for static applications.