Dimensional reduction in nonlinear filtering: A homogenization approach
Probability
2013-12-03 v2 Computation
Abstract
We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system. We prove that the nonlinear filter converges to our homogenized filter with rate . This is achieved by a suitable asymptotic expansion of the dual of the Zakai equation, and by probabilistically representing the correction terms with the help of BDSDEs.
Cite
@article{arxiv.1112.2986,
title = {Dimensional reduction in nonlinear filtering: A homogenization approach},
author = {Peter Imkeller and N. Sri Namachchivaya and Nicolas Perkowski and Hoong C. Yeong},
journal= {arXiv preprint arXiv:1112.2986},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AAP901 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)