# Variance Decay Property for Filter Stability

arXiv: https://arxiv.org/abs/2305.12850 · HTML: https://mlsanity.com/paper/2305.12850/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2023.

## Built on by (most cited first, 1 of 1)

- [Dual Filter: A Transformer-like Inference Architecture for Hidden Markov Models](https://mlsanity.com/paper/2505.00818/) (2025)

## Abstract (arXiv)

This paper is concerned with the problem of nonlinear (stochastic) filter stability of a hidden Markov model (HMM) with white noise observations. A contribution is the variance decay property which is used to conclude filter stability. For this purpose, a new notion of the Poincar'e inequality (PI) is introduced for the nonlinear filter. PI is related to both the ergodicity of the Markov process as well as the observability of the HMM. The proofs are based upon a recently discovered minimum variance duality which is used to transform the nonlinear filtering problem into a stochastic optimal control problem for a backward stochastic differential equation (BSDE).