Title :
Rare event simulation for a generalized Hawkes process
Author :
Zhang, Xiao-Wei ; Glynn, Peter W. ; Giesecke, Kay ; Blanchet, Jose
Author_Institution :
Dept. of Manage. Sci. & Eng., Stanford Univ., Stanford, CA, USA
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.
Keywords :
affine transforms; importance sampling; probability; Gartner-Ellis asymptotic regime; affine point process; exponential martingale; generalized Hawkes process; importance sampling algorithm; rare event simulation; tail probability; Clustering algorithms; Differential equations; Discrete event simulation; Engineering management; Fourier transforms; Industrial engineering; Monte Carlo methods; Operations research; Tail; Timing;
Conference_Titel :
Simulation Conference (WSC), Proceedings of the 2009 Winter
Conference_Location :
Austin, TX
Print_ISBN :
978-1-4244-5770-0
DOI :
10.1109/WSC.2009.5429693
