Preprints, Working Papers, ... Year : 2025

Approximation of non-linear Markov chains using diffusion approximations: L^1-norm estimate and application to adipose cell modelling

Léo Meyer

Abstract

We introduce a class of continuous in time non-linear Markov chains with application in different applied fields such has epidemics, opinion spreading or cells dynamics. This Markov chains depends on a parameter ε which is meant to go to zero, and in the limit the Markov chains tends to a deterministic ordinary differential equation. We show that such Markov chains are 'well approximated' by diffusion approximations as in the classical result from [Kurtz, 1978], meaning that the rate of convergence to this diffusion approximation is better than the one to the deterministic limit. Particularly, our results suggests that for some application where the scaling parameter has a physical interpretation and should remain strictly positive, the diffusion approximation is more adapted to study macroscopic scale dynamics. We present an application of our result to adipose cell size dynamics.
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Dates and versions

hal-04877614 , version 1 (09-01-2025)

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  • HAL Id : hal-04877614 , version 1

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Léo Meyer. Approximation of non-linear Markov chains using diffusion approximations: L^1-norm estimate and application to adipose cell modelling. 2025. ⟨hal-04877614⟩
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