On a role of predictor in the filtering stability
Pavel Chigansky, The Weizmann Institute of Science
Robert Liptser, Tel Aviv University
Abstract
When is a nonlinear filter stable with respect to its initial
condition? In spite of the recent progress, this question still
lacks a complete answer in general. Currently available results
indicate that stability of the filter depends on the signal
ergodic properties and the observation process regularity and may
fail if either of the ingredients is ignored. In this note we
address the question of stability in a particular weak sense and
show that the estimates of certain functions are always stable.
This is verified without dealing directly with the filtering
equation and turns to be inherited from certain one-step predictor
estimates.
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona.
The preferred way is to send a scanned (jpeg or pdf) copy of the signed copyright form to the managing editor Philippe Carmona at ejpecpme@math.univ-nantes.fr.
If a paper has several authors, the corresponding author signs the copyright form
on behalf of all the authors.