Moderate deviations for particle filtering

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dc.creatorDouc, R.
dc.creatorGuillin, A.
dc.creatorNajim, J.
dc.date2004-01-07
dc.date2005-04-06
dc.date.accessioned2026-07-07T05:04:24Z
dc.date.available2026-07-07T05:04:24Z
dc.descriptionConsider the state space model (X_t,Y_t), where (X_t) is a Markov chain, and (Y_t) are the observations. In order to solve the so-called filtering problem, one has to compute L(X_t|Y_1,...,Y_t), the law of X_t given the observations (Y_1,...,Y_t). The particle filtering method gives an approximation of the law L(X_t|Y_1,...,Y_t) by an empirical measure \frac{1}{n}\sum_1^nδ_{x_{i,t}}. In this paper we establish the moderate deviation principle for the empirical mean \frac{1}{n}\sum_1^nψ(x_{i,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.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051604000000657 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0401058
dc.identifierhttp://arxiv.org/abs/math/0401058
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 1B, 587-614
dc.identifierdoi:10.1214/105051604000000657
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69791
dc.subjectProbability
dc.subject60F10, 60G35, 93E11 (Primary)
dc.titleModerate deviations for particle filtering
dc.typetext

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