On the Lyapunov Foster criterion and Poincare inequality for Reversible Markov Chains

Amirhossein Taghvaei, Prashant G. Mehta

Research output: Contribution to journalArticlepeer-review

Abstract

This paper 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: (i) it relies entirely on functional-analytic non-probabilistic arguments; and (ii) it makes explicit the connection between a Foster-Lyapunov function and Poincare inequality. The proof is used to derive an explicit bound for the spectral gap. An extension to the non-reversible case is also presented.

Original languageEnglish (US)
Pages (from-to)2605-2609
Number of pages5
JournalIEEE Transactions on Automatic Control
Volume67
Issue number5
DOIs
StateAccepted/In press - 2021

Keywords

  • Convergence
  • Eigenvalues and eigenfunctions
  • Kernel
  • Lyapunov methods
  • Markov processes
  • Mechanical variables measurement
  • Stability criteria

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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