Rare event estimation for a large-scale stochastic hybrid system with air traffic application

Embedding of rare event estimation theory within a stochastic analysis framework has recently led to signi��?cant novel results in rare event estimation for a diffusion process using sequential MC simulation. This chapter presents this rare event estimation theory for diffusions to a Stochastic Hybrid System (SHS) and extends it in order to handle a large scale SHS where a very huge number of rare discrete modes may contribute signi��?cantly to the rare event estimation. Essentially, the approach taken is to introduce a suitable aggregation of the discrete modes, and to develop importance sampling and Rao-Blackwellization relative to these aggregated modes. The practical use of this approach is demonstrated for the stimation of mid-air collision for an advanced air traf��?c control example.