We study the properties of a nonlinear model of filtering in discrete time which leads to explicit computations. The signal is a standard AR(1) process, but noises are multiplicative and non-Gaussian. If the initial distribution of the AR(1) process is taken to belong to a specified class, the prediction and optimal filters also belong to this class and the prediction and updating steps are explicit. We prove the existence of a stationary version for the prediction filter and complete the theoretical study with simulations to illustrate the behaviour of the filter.
Publié le : 2004-08-14
Classification:
discrete time observations,
filtering,
hidden Markov models,
multiplicative noise,
stability of the filtering algorithm
@article{1093265637,
author = {Genon-Catalot, Valentine and Kessler, Mathieu},
title = {Random scale perturbation of an AR(1) process and its properties as a nonlinear explicit filter},
journal = {Bernoulli},
volume = {10},
number = {2},
year = {2004},
pages = { 701-720},
language = {en},
url = {http://dml.mathdoc.fr/item/1093265637}
}
Genon-Catalot, Valentine; Kessler, Mathieu. Random scale perturbation of an AR(1) process and its properties as a nonlinear explicit filter. Bernoulli, Tome 10 (2004) no. 2, pp. 701-720. http://gdmltest.u-ga.fr/item/1093265637/