Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

2016/07/26

13:00-14:30   Room #052 (Graduate School of Math. Sci. Bldg.)
Ajay Jasra (National University of Singapore)
Multilevel Particle Filters
[ 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 $\cO(\varepsilon^2)$ mean-square error between
the multilevel estimator and average with respect to the filtering
distribution is shown to scale optimally, for example as
$\cO(\varepsilon^{-2})$ for optimal rates of convergence of the
underlying diffusion approximation.
The method is illustrated on several examples.