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

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Abstract

We construct a stationary Markov process with trivial tail σ-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 σ-fields is taken for granted.

Original languageEnglish (US)
Pages (from-to)763-784
Number of pages22
JournalIsrael Journal of Mathematics
Volume192
Issue number2
DOIs
StatePublished - Mar 28 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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