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| HAL: hal-00293422, version 1 |
| arXiv: 0807.0749 |
| DOI: 10.1016/j.spa.2010.07.002 |
| Detailed view |  Export this paper |
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| Stochastic Processes and their Applications 120, 12 (2010) 2495-2519 |
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| Detection of cellular aging in a Galton-Watson process |
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| Jean-François Delmas 1Laurence Marsalle 2 |
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| (2010-12) |
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| We consider the bifurcating Markov chain model introduced by Guyon to detect cellular aging from cell lineage. To take into account the possibility for a cell to die, we use an underlying Galton-Watson process to describe the evolution of the cell lineage. We give in this more general framework a weak law of large number, an invariance principle and thus fluctuation results for the average over one generation or up to one generation. We also prove the fluctuations over each generation are independent. Then we present the natural modifications of the tests given by Guyon in cellular aging detection within the particular case of the auto-regressive model. |
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| 1: | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| 2: | Laboratoire Paul Painlevé (LPP) |
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CNRS : UMR8524 – Université Lille I - Sciences et technologies |
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| Subject | : | Mathematics/Probability |
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| Aging – Galton-Watson process – bifurcating Markov process – stable convergence |
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| hal-00293422, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00293422 | |
| oai:hal.archives-ouvertes.fr:hal-00293422 | |
| From: Jean-François Delmas | |
| Submitted on: Friday, 4 July 2008 15:07:46 | |
| Updated on: Wednesday, 2 November 2011 17:00:31 | |
