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On the Lyapunov Foster Criterion and Poincaré Inequality for Reversible Markov Chains.
- Source :
-
IEEE Transactions on Automatic Control . May2022, Vol. 67 Issue 5, p2605-2609. 5p. - Publication Year :
- 2022
-
Abstract
- This article presents an elementary proof of stochastic stability of a discrete-time reversible Markov chain starting from a Foster–Lyapunov drift condition. Besides its relative simplicity, there are two salient features of the proof. 1) It relies entirely on functional-analytic non-probabilistic arguments. 2) It makes explicit the connection between a Foster–Lyapunov function and Poincaré inequality. The proof is used to derive an explicit bound for the spectral gap. An extension to the nonreversible case is also presented. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MARKOV processes
*STABILITY criterion
Subjects
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 67
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 156630403
- Full Text :
- https://doi.org/10.1109/TAC.2021.3089643