Mathematics > Probability
[Submitted on 5 Dec 2018 (v1), last revised 7 Dec 2022 (this version, v6)]
Title:Stochastic Observability and Filter Stability under Several Criteria
View PDFAbstract:Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for stochastic non-linear dynamical systems which involves an explicit functional characterization. To justify its operational use, we establish that this definition implies filter stability under mild continuity conditions: an incorrectly initialized non-linear filter is said to be stable if the filter eventually corrects itself with the arrival of new measurement information. Numerous examples are presented and a detailed comparison with the literature is reported. We also establish implications for various criteria for filter stability under several notions of convergence such as weak convergence, total variation, and relative entropy. These findings are connected to robustness and approximations in partially observed stochastic control.
Submission history
From: Curtis McDonald [view email][v1] Wed, 5 Dec 2018 01:29:38 UTC (28 KB)
[v2] Tue, 8 Jan 2019 18:02:09 UTC (31 KB)
[v3] Fri, 18 Oct 2019 15:35:18 UTC (221 KB)
[v4] Thu, 23 Jan 2020 16:31:17 UTC (34 KB)
[v5] Mon, 6 Jul 2020 15:42:34 UTC (145 KB)
[v6] Wed, 7 Dec 2022 15:50:48 UTC (46 KB)
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