Ergodic Behavior of Non-conservative Semigroups via Generalized Doeblin’s Conditions

By Vincent Bansaye, Bertrand Cloez, Pierre Gabriel. Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, 2017

64 citations recorded by the source corpus.

We provide quantitative estimates in total variation distance for positive semigroups, 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 inherited from Champagnat and Villemonais (Probab. Theory Relat. Fields 164(1–2):243–283, 2016) 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 semigroups and new bounds in the homogeneous setting. They are illustrated on the renewal equation.

Subfields: Finance, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/7f16ada2700fea3cc32701884cbadc24cdd1ece6

How researchers see this paper

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In Finance

1. Vincent Bansaye
2. Pierre Gabriel
3. Aline Marguet
4. Bertrand Cloez
5. Jinghai Shao

In Mathematical Physics

1. Bertrand Cloez
2. Vincent Bansaye
3. Aline Marguet
4. Pierre Gabriel

In Molecular Biology

1. Bertrand Cloez
2. Vincent Bansaye

Citations in the corpus

• A non‐conservative Harris ergodic theorem (2019, methodology): “Using (A3) and (A4) and following [20, 7], we prove a Doeblin condition (2.”