Moderate deviations for particle filtering
Douc, R. ; Guillin, A. ; Najim, J.
Ann. Appl. Probab., Tome 15 (2005) no. 1A, p. 587-614 / Harvested from Project Euclid
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.
Publié le : 2005-02-14
Classification:  Particle filters,  moderate deviation principle,  60F10,  60G35,  93E11
@article{1107271661,
     author = {Douc, R. and Guillin, A. and Najim, J.},
     title = {Moderate deviations for particle filtering},
     journal = {Ann. Appl. Probab.},
     volume = {15},
     number = {1A},
     year = {2005},
     pages = { 587-614},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1107271661}
}
Douc, R.; Guillin, A.; Najim, J. Moderate deviations for particle filtering. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp.  587-614. http://gdmltest.u-ga.fr/item/1107271661/