Volume 19, 2015
|Page(s)||482 - 501|
|Published online||11 November 2015|
Quantitative speeds of convergence for exposure to food contaminants
UMR 6625 CNRS Institut de Recherche Mathématique de Rennes
(IRMAR), Université de Rennes 1, Campus de Beaulieu, 35042
Received: 16 October 2013
Revised: 11 June 2014
In this paper, we consider a class of piecewise-deterministic Markov processes modeling the quantity of a given food contaminant in the body. On the one hand, the amount of contaminant increases with random food intakes and, on the other hand, decreases thanks to the release rate of the body. Our aim is to provide quantitative speeds of convergence to equilibrium for the total variation and Wasserstein distances via coupling methods.
Mathematics Subject Classification: 60J25 / 60K15 / 60B10
Key words: Piecewise deterministic Markov processes / coupling / renewal Markov processes / convergence to equilibrium / exponential ergodicity / dietary contamination
© EDP Sciences, SMAI, 2015
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