Markov kernels under minorization and modulated drift conditions - Centre Henri Lebesgue
Pré-Publication, Document De Travail Année : 2024

Markov kernels under minorization and modulated drift conditions

Résumé

This paper is devoted to the study of Markov kernels on general measurable space under first-order minorization condition and modulated drift condition. The following issues can be 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. All theses issues are discussed in the present document except the perturbation schemes and the non-geometric rate of convergence of iterates, both which will be included soon to form our final text. All the results reported here focus on Markov kernels using a residual kernel approach. This turns out to be a very simple and efficient way to deal with all mentioned issues on Markov kernels. In particular, the document is essentially self-contained.

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Dates et versions

hal-04753237 , version 1 (25-10-2024)

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  • HAL Id : hal-04753237 , version 1

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Loïc Hervé, James Ledoux. Markov kernels under minorization and modulated drift conditions. 2024. ⟨hal-04753237⟩
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