Section: Application Domains
Rare event simulation
See 3.4 , 6.3 , 6.4 , 6.5 , 6.6 , 6.9 , 7.1 , 7.3 and 7.7 .
Another application domain of particle methods, or interacting Monte Carlo methods, that ASPI has decided to focus on is the estimation of the small probability of a rare but critical event, in complex dynamical systems. This is a crucial issue in industrial areas such as
nuclear power plants, food industry, telecommunication networks, finance and insurance industry, air traffic management, etc.
In such complex systems, analytical methods cannot be used, and naive Monte Carlo methods are clearly unefficient to estimate accurately very small probabilities. Besides importance sampling, an alternate widespread technique consists in multilevel splitting  , where trajectories going towards the critical set are given offsprings, thus increasing the number of trajectories that eventually reach the critical set. This approach not only makes it possible to estimate the probability of the rare event, but also provides realizations of the random trajectory, given that it reaches the critical set, i.e. provides realizations of typical critical trajectories, an important feature that methods based on importance sampling usually miss.
ASPI is contributing to several applications of multilevel splitting for rare event simulation, such as risk assessment in air traffic management, see 7.1 , detection in sensor networks, see 7.3 , protection of digital documents, see 7.7 , and credit risk estimation.