Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions
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Publication:2306741
DOI10.1007/S10440-019-00253-5zbMATH Open1442.47030arXiv1710.05584OpenAlexW2766813240WikidataQ128093303 ScholiaQ128093303MaRDI QIDQ2306741
Author name not available (Why is that?)
Publication date: 24 March 2020
Published in: (Search for Journal in Brave)
Abstract: We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and Doeblin's type conditions for coupling the associated process. Our aim is to provide quantitative estimates for linear partial differential equations and we develop several applications for population dynamics in varying environment. We start with the asymptotic profile for a growth diffusion model with time and space non-homogeneity. Moreover we provide general estimates for semigroups which become asymptotically homogeneous, which are applied to an age-structured population model. Finally, we obtain a speed of convergence for periodic semi-groups and new bounds in the homogeneous setting. They are are illustrated on the renewal equation.
Full work available at URL: https://arxiv.org/abs/1710.05584
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