滤波理论中σ-域的交与上确界的交换
On the exchange of intersection and supremum of sigma-fields in filtering theory
摘要：
本文构造了一个具有平凡尾σ-域的平稳马尔可夫过程和一个非退化观测过程，使得相应的非线性滤波过程不是唯一遍历的。这解决了作者在非线性滤波遍历论中的一个否定猜想，该猜想是由H. Kunita（1971），其中σ-域的交和上确界的交换被认为是理所当然的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
