Multilevel particle filter

Understand

In this paper 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 $\mathcal{O}(\varepsilon^2)$ mean-square error between the multilevel estimator and average with respect to the filtering distribution is shown to scale optimally, for example as $\mathcal{O}(\varepsilon^{-2})$ for optimal rates of convergence of the underlying diffusion approximation.