## The Annals of Applied Probability

### Moderate deviations for particle filtering

#### Abstract

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

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

Dates
First available in Project Euclid: 1 February 2005

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

Digital Object Identifier
doi:10.1214/105051604000000657

Mathematical Reviews number (MathSciNet)
MR2114983

Zentralblatt MATH identifier
1072.60018

#### Citation

Douc, R.; Guillin, A.; Najim, J. Moderate deviations for particle filtering. Ann. Appl. Probab. 15 (2005), no. 1B, 587--614. doi:10.1214/105051604000000657. https://projecteuclid.org/euclid.aoap/1107271661

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