Moderate deviations for particle filtering

Douc, Randal; Guillin, Arnaud; Najim, J.

Douc, Randal; Guillin, Arnaud; Najim, J. (2005), Moderate deviations for particle filtering, The Annals of Applied Probability, 15, 1B, p. 587-614. http://dx.doi.org/10.1214/105051604000000657

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Type

Article accepté pour publication ou publié

External document link

http://projecteuclid.org/euclid.aoap/1107271661

Date

2005

Journal name

The Annals of Applied Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

587-614

Abstract (EN)

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.

Subjects / Keywords

Particle filters; moderate deviation principle