Rare Event Simulation for a Generalized Hawkes Process

X. Zhang, J. H. Blanchet, K. Giesecke, and P. W. Glynn

Proceedings of the 2009 Winter Simulation Conference, 1291-1298 (2009)

In this paper we study rare event simulation for the tail probability of an affine point process (Jt)t≥0 that generalizes the Hawkes process. By constructing a suitable exponential martingale, we are able to construct an importance sampling algorithm that is logarithmically efficient in the Gartner-Ellis asymptotic regime.