統計数学セミナー
Seminar on Probability and Statistics
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Seminar on Probability and Statistics
Tuesday July 26 2016
Osaka I204
1:00-2:30 pm


Multilevel Particle Filters


Ajay Jasra
National University of Singapore

Abstract

In this talk the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by $l$. A multilevel estimator is proposed, consisting of a telescopic sum of increment estimators associated to the successive levels. The work associated to $\cO( arepsilon^2)$ mean-square error between the multilevel estimator and average with respect to the filtering distribution is shown to scale optimally, for example as $\cO( arepsilon^{-2})$ for optimal rates of convergence of the underlying diffusion approximation. The method is illustrated on several examples.




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Seminar on Probability and Statistics