大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Multilevel Particle Filters

Ajay Jasra (National University of Singapore)

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4. Multilevel Particle Filters

大阪大学 数理・データ科学セミナー　データ科学セミナシリーズ 第13回　（CREST JST共催）

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(ε²) mean-square error between the multilevel estimator and average with respect to the filtering distribution is shown to scale optimally, for example as cO(1/ε²) for optimal rates of convergence of the underlying diffusion approximation.
The method is illustrated on several examples.