On the exchange of intersection and supremum of sigma-fields in filtering theory
Probability
2013-01-29 v2 Dynamical Systems
Abstract
We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.
Keywords
Cite
@article{arxiv.1009.0507,
title = {On the exchange of intersection and supremum of sigma-fields in filtering theory},
author = {Ramon van Handel},
journal= {arXiv preprint arXiv:1009.0507},
year = {2013}
}
Comments
20 pages