Polynomial Convergence Rates for Markov Kernels Under Nested Modulated Drift Conditions

Loïc Hervé () and James Ledoux ()
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Loïc Hervé: Univ Rennes, INSA Rennes, CNRS, IRMAR-UMR 6625
James Ledoux: Univ Rennes, INSA Rennes, CNRS, IRMAR-UMR 6625

Journal of Theoretical Probability, 2025, vol. 38, issue 3, 1-22

Abstract: Abstract When a Markov kernel P satisfies a minorization condition and nested modulated drift conditions, Jarner and Roberts provided an asymptotic polynomial convergence rate in weighted total variation norm of $$P^n(x,\cdot )$$ P n ( x , · ) to the invariant probability measure $$\pi $$ π of P. In connection with this polynomial asymptotic, we propose explicit and simple estimates on series of such weighted total variation norms, from which an estimate for the total variation norm of $$P^n(x,\cdot )-\pi $$ P n ( x , · ) - π is deduced. The proofs are self-contained and based on the residual kernel and the Nummelin-type representation of $$\pi $$ π . No coupling technique is used.

Keywords: Drift conditions; Invariant probability measure; Minorization condition; Residual kernel; 60J05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01416-x

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