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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.

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Authors and Affiliations

  1. Princeton University, Sherrerd Hall 227, Princeton, NJ, 08544, USA

    Ramon van Handel

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  1. Ramon van Handel
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Correspondence to Ramon van Handel.

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This work was partially supported by NSF grant DMS-1005575.

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van Handel, R. On the exchange of intersection and supremum of σ-fields in filtering theory. Isr. J. Math. 192, 763–784 (2012). https://doi.org/10.1007/s11856-012-0045-9

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  • DOI: https://doi.org/10.1007/s11856-012-0045-9

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