This thesis is a large deviations study 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 analysis of related algorithms, for interacting article 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.
Cai, Yi,
"Analysis of An Interacting Particle Method for Rare Event Estimation"
(2012).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0GT5KGW
