On the exchange of intersection and supremum of sigma-fields in filtering theory

Details On the exchange of intersection and supremum of sigma-fields in filtering theory On the exchange of intersection and supremum of sigma-fields in filtering theory

2010-09-02

arxiv.org/abs/1009.0507v2

Mathematics

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20 pages

Scientific paper

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.

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