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A Probabilistic Look at Conservative Growth-Fragmentation Equations

  • Florian Bouguet
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2215)

Abstract

In this note, we consider general growth-fragmentation equations from a probabilistic point of view. Using Foster-Lyapunov techniques, we study the recurrence of the associated Markov process depending on the growth and fragmentation rates. We prove the existence and uniqueness of its stationary distribution, and we are able to derive precise bounds for its tails in the neighborhoods of both 0 and + . This study is systematically compared to the results obtained so far in the literature for this class of integro-differential equations.

Keywords

Growth-fragmentation Markov process Stationary measure Tail of distribution Foster-Lyapunov criterion. 

Notes

Acknowledgements

The author wants to thank Pierre Gabriel for fruitful discussions about growth-fragmentation equations, as well as Eva Löcherbach, Florent Malrieu and Jean-Christophe Breton for their precious help and comments. The referee is also warmly thanked for his constructive remarks. This work was financially supported by the ANR PIECE (ANR-12-JS01-0006-01), and the Centre Henri Lebesgue (programme “Investissements d’avenir” ANR-11-LABX-0020-01).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université de Lorraine, IECL, UMR 7502Vandœuvre-lès-NancyFrance
  2. 2.CNRS, IECL, UMR 7502Vandœuvre-lès-NancyFrance
  3. 3.InriaVillers-lès-NancyFrance

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