2024/05/02 by Jin Won Kim, Kim, Jin Won, Anant A. Joshi +3 · 1 citation
Engineering · Physics and Astronomy · #Advanced Algorithms and Applications #FOS: Mathematics #Hydraulic and Pneumatic Systems #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2405.01127
openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, a backward map is introduced for the purposes of analysis of the nonlinear (stochastic) filter stability. The backward map is important because the filter-stability in the sense of \chisq-divergence follows from showing a certain variance decay property for the backward map. To show this property requires additional assumptions on the model properties of the hidden Markov model (HMM). The analysis in this paper is based on introducing a Poincaré Inequality (PI) for HMMs with white noise observations. In finite state-space settings, PI is related to both the ergodicity of the Markov process as well as the observability of the HMM. It is shown that the Poincaré constant is positive if and only if the HMM is detectable.