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arXiv:2211.02032 (math)
[Submitted on 3 Nov 2022 (v1), last revised 1 Oct 2024 (this version, v3)]

Title:To spike or not to spike: the whims of the Wonham filter in the strong noise regime

Authors:Cédric Bernardin, Reda Chhaibi, Joseph Najnudel, Clément Pellegrini
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Abstract:We study the celebrated Shiryaev-Wonham filter (1964) in its historical setup where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations.
Earlier results of the authors show the appearance of spikes in the filtered process, akin to a metastability phenomenon. This paper is aimed at understanding the smoothed optimal filter, which is relevant for any system with feedback. In particular, we exhibit a sharp phase transition between a spiking regime and a regime with perfect smoothing.
Comments: v1, v2: Preliminary versions. v3: Submitted version
Subjects: Probability (math.PR); Information Theory (cs.IT); Optimization and Control (math.OC); Statistics Theory (math.ST)
Cite as: arXiv:2211.02032 [math.PR]
  (or arXiv:2211.02032v3 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2211.02032

Submission history

From: Reda Chhaibi [view email]
[v1] Thu, 3 Nov 2022 17:52:13 UTC (346 KB)
[v2] Sun, 23 Apr 2023 23:34:31 UTC (346 KB)
[v3] Tue, 1 Oct 2024 08:20:39 UTC (431 KB)
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