Multilevel particle filter

Ajay Jasra; Kengo Kamatani; Kody J. H. Law; Yan Zhou

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arXiv · 1510.04977

Multilevel particle filter

Ajay Jasra·Kengo Kamatani·Kody J. H. Law·Yan Zhou

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Abstract

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. The method is illustrated on some toy examples as well as estimation of interest rate based on real S&P 500 stock price data.

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Ajay Jasra, Kengo Kamatani, Kody J. H. Law, Yan Zhou. 2015-10-16. Multilevel particle filter. https://arxiv.org/abs/1510.04977

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