The Annals of Applied Probability

Moderate deviations for particle filtering

R. Douc, A. Guillin, and J. Najim

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Consider the state space model (Xt,Yt), where (Xt) is a Markov chain, and (Yt) are the observations. In order to solve the so-called filtering problem, one has to compute ℒ(Xt|Y1,…,Yt), the law of Xt given the observations (Y1,…,Yt). The particle filtering method gives an approximation of the law ℒ(Xt|Y1,…,Yt) by an empirical measure $\frac{1}{n}$∑1nδxi,t. In this paper we establish the moderate deviation principle for the empirical mean $\frac{1}{n}$∑1nψ(xi,t) (centered and properly rescaled) when the number of particles grows to infinity, enhancing the central limit theorem. Several extensions and examples are also studied.

Article information

Ann. Appl. Probab., Volume 15, Number 1B (2005), 587-614.

First available in Project Euclid: 1 February 2005

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 93E11: Filtering [See also 60G35]

Particle filters moderate deviation principle


Douc, R.; Guillin, A.; Najim, J. Moderate deviations for particle filtering. Ann. Appl. Probab. 15 (2005), no. 1B, 587--614. doi:10.1214/105051604000000657.

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