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, Volume 24, Issue 2, pp 341–360 | Cite as

Semi-parametric inference for the absorption features of a growth-fragmentation model

  • Romain Azaïs
  • Alexandre Genadot
Original Paper

Abstract

In the present paper, we focus on semi-parametric methods for estimating the absorption probability and the distribution of the absorbing time of a growth-fragmentation model observed within a long time interval. We establish that the absorption probability is the unique solution in an appropriate space of a Fredholm equation of the second kind whose parameters are unknown. We estimate this important characteristic of the underlying process by solving numerically the estimated Fredholm equation. Even if the study has been conducted for a particular model, our method is quite general.

Keywords

Non-ergodic piecewise-deterministic Markov process  Growth-fragmentation process Semi-parametric estimation Absorption probability Fredholm integral equation 

Mathematics Subject Classification

62M05 93C30 62G05 

Notes

Acknowledgments

The referees deserve thanks for careful reading of the original version of the manuscript and many helpful suggestions for improvement in the article. The authors also acknowledge Alexandre Boumezoued for fruitful discussions about hybrid processes and Poisson random measures.

Supplementary material

11749_2014_410_MOESM1_ESM.pdf (289 kb)
ESM 1 (PDF 289 kb)

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2014

Authors and Affiliations

  1. 1.Inria Nancy-Grand Est, Team BIGS, Institut Élie Cartan de LorraineVandoeuvre-lès-NancyFrance
  2. 2.CEREMADE UMR 7534, Université Paris-DauphineParisFrance

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