
Moderate deviations for particle filtering
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
Type
Article accepté pour publication ou publiéExternal document link
http://projecteuclid.org/euclid.aoap/1107271661Date
2005Journal name
The Annals of Applied ProbabilityVolume
15Number
1BPublisher
Institute of Mathematical Statistics
Pages
587-614
Publication identifier
Metadata
Show full item recordAbstract (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 principleRelated items
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