In Crisan, Gaines and Lyons [SIAM J. Appl. Probab.
58 (1998) 313--342] we describe a branching particle algorithm that produces a
particle approximation to the solution of the Zakai equation and find an
upper bound for the rate of convergence of the mean square error. In this
paper, the exact rate of convergence of the mean square error is deduced.
Also, several variations of the branching algorithm with better rates of
convergence are introduced.
Publié le : 2003-04-14
Classification:
Zakai equation,
branching algorithm,
particle filters,
filtering,
Monte Carlo approximation,
93E11,
60G57,
65U05
@article{1048516533,
author = {Crisan, Dan},
title = {Exact rates of convergeance for a branching particle approximation to the solution of the Zakai equation},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 693-718},
language = {en},
url = {http://dml.mathdoc.fr/item/1048516533}
}
Crisan, Dan. Exact rates of convergeance for a branching particle approximation to the solution of the Zakai equation. Ann. Probab., Tome 31 (2003) no. 1, pp. 693-718. http://gdmltest.u-ga.fr/item/1048516533/