Irreducible Markov kernels: a residual kernel approach
Abstract
The Markov kernels on general measurable space are studied under a first-order minorization condition and a modulated drift condition. The following issues are addressed: Existence and uniqueness of invariant measures, recurrence/transience properties including Harris-recurrence property, convergence in total variation of iterates, Poisson's equation, perturbation schemes and rate of convergence of iterates including the so-called geometric ergodicity. Extensions under multi-minorization conditions are also discussed with a focus on solutions to Poisson's equation. All the material on Markov kernels provided here is based on a residual kernel approach. This is a simple and efficient way to deal with all mentioned issues. It turns out that this book is essentially self-contained.
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BibTeX
@misc{loic2026irreducible,
title = {{Irreducible Markov kernels: a residual kernel approach}},
author = {Hervé Loïc and James Ledoux},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05753489v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Irreducible Markov kernels: a residual kernel approach
AU - Hervé Loïc
AU - James Ledoux
PY - 2026
DA - 2026/09/16
PB - HAL
UR - https://hal.science/hal-05753489v1
AB - The Markov kernels on general measurable space are studied under a first-order minorization condition and a modulated drift condition. The following issues are addressed: Existence and uniqueness of invariant measures, recurrence/transience properties including Harris-recurrence property, convergence in total variation of iterates, Poisson's equation, perturbation schemes and rate of convergence of iterates including the so-called geometric ergodicity. Extensions under multi-minorization conditions are also discussed with a focus on solutions to Poisson's equation. All the material on Markov kernels provided here is based on a residual kernel approach. This is a simple and efficient way to deal with all mentioned issues. It turns out that this book is essentially self-contained.
ER -