A variational principle in probabilistic dynamics

Probabilistic dynamics offers a theoretical framework for an integrated treatment of accident sequences. But such realistic modelling in risk analysis calls for the development of efficient numerical schemes, in order to benefit from the conceptual advantages it provides. Up to now, mostly simulation techniques have been envisioned to deal with this kind of problem. However, a sufficiently exhaustive search for scenarios and the low probability of the situations of interest limit the efficiency of these methods. This work, therefore, explores an alternative approach, based on a variationally processed correction of a reliability characteristic, first estimated with an approximation of the probability field. This first estimation can result either from the solution of a simplified problem or from the output of another solution scheme. A variational principle for the evaluation of a functional of the probability distribution in this dynamic context is established. The possible achievements as well as the limitations of this new approach are discussed, starting from the results obtained for two test-cases