The Conditional Poincar\'e Inequality for Filter Stability
Probability
2021-10-12 v2 Optimization and Control
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.
Cite
@article{arxiv.2103.14631,
title = {The Conditional Poincar\'e Inequality for Filter Stability},
author = {Jin Won Kim and Prashant G. Mehta and Sean Meyn},
journal= {arXiv preprint arXiv:2103.14631},
year = {2021}
}
Comments
60th IEEE Conference on Decision and Control (CDC)