Analysis of an interacting particle method for rare event estimation

Authors:
Yi Cai;Paul Dupuis
Affiliations:
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, USA 02912;Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, USA 02912
Venue:
Queueing Systems: Theory and Applications
Year:
2013

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Abstract

We present a large deviations analysis for the performance of an interacting particle method for rare event estimation. The analysis is restricted to a one-dimensional setting, though even in this restricted setting a number of new techniques must be developed. In contrast to the large deviations analyses of related algorithms, for interacting particle schemes it is an occupation measure analysis that is relevant, and within this framework many standard assumptions (stationarity, Feller property) can no longer be assumed. The methods developed are not limited to the question of performance analysis, and in fact give the full large deviations principle for such systems.