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Blom, H.A.P. and Bakker, G.J. and Krystul, J.
(2009)
Rare event estimation for a large-scale stochastic hybrid system with air traffic application.
In:
Rare Event Simulation using Monte Carlo Methods.
John Wiley & Sons, pp. 193-214.
ISBN 978-0-470-77269-0
Full text available as:
Official URL: http://dx.doi.org/10.1002/9780470745403.ch9  AbstractEmbedding 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.
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