论文标题
要尖峰或不升高：在强噪声方面，旺姆过滤器的异想天开
To spike or not to spike: the whims of the Wonham filter in the strong noise regime
论文作者
论文摘要
我们在其历史设置中研究了著名的Shiryaev-Wonham Filter（1964），其中隐藏的马尔可夫跳跃过程具有两个州。我们对观察方程的噪声状态较弱感兴趣。有趣的是，这成为过滤方程的强大噪声状态。 作者的早期结果显示了在过滤过程中的尖峰出现，类似于亚算光。本文旨在理解平滑的最佳过滤器，这与任何反馈的系统有关。特别是，我们在尖峰状态与具有完美平滑状态的机制之间表现出急剧的相变。
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.
