Rare event simulation for a generalized Hawkes process

Authors:
Xiao-Wei Zhang;Peter W. Glynn;Kay Giesecke;Jose Blanchet
Affiliations:
Stanford University, Stanford, C. A.;Stanford University, Stanford, C. A.;Stanford University, Stanford, C. A.;Columbia University, New York, N. Y.
Venue:
Winter Simulation Conference
Year:
2009

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Introduction to Rare Event Simulation

Introduction to Rare Event Simulation

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Abstract

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.