@inproceedings{38fae6ba19674c73b2d38963101e321d,
title = "The Conditional Poincar{\'e} Inequality for Filter Stability",
abstract = "This paper is concerned with the problem of nonlinear filter stability of ergodic Markov processes. The main contribution is the conditional Poincar{\'e} inequality (PI), which is shown to yield filter stability. The proof is based upon a recently discovered duality which is used to transform the nonlinear filtering problem into a stochastic optimal control problem for a backward stochastic differential equation (BSDE). Based on these dual formalisms, a comparison is drawn between the stochastic stability of a Markov process and the filter stability. The latter relies on the conditional PI described in this paper, whereas the former relies on the standard form of PI. ",
author = "{Won Kim}, Jin and Mehta, {Prashant G.} and Sean Meyn",
note = "Funding Information: Financial support from the NSF grant 1761622 and the ARO grant W911NF1810334 is gratefully acknowledged. Publisher Copyright: {\textcopyright} 2021 IEEE.; 60th IEEE Conference on Decision and Control, CDC 2021 ; Conference date: 13-12-2021 Through 17-12-2021",
year = "2021",
doi = "10.1109/CDC45484.2021.9682849",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1629--1636",
booktitle = "60th IEEE Conference on Decision and Control, CDC 2021",
address = "United States",
}