Stochastic and Physics-Based Simulation of Extreme Situations

This chapter addresses two alternative approaches to extreme situations, which may be useful when the lack of extreme observations severely limits the relevance of a purely statistical approach. The first methodology is based on stochastic modeling of the regular phenomenon, for example, via autoregressive processes. Capturing this phenomenon allows extrapolation to extreme values based on theoretical properties of stochastic processes. The second approach is based on the use, by Monte Carlo-based methods, of numerical simulation models implementing the physical equations representing the phenomenon under study. This second approach, which is originally used in structural reliability, requires the development of specific simulation techniques that focus on very low-probability events; it appears to be more and more appropriate as expert knowledge of the phenomena increases.