On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models

Fabien Campillo 1 Nicolas Champagnat 2, 3 Coralie Fritsch 2, 4, 3
1 MATHNEURO - Mathématiques pour les Neurosciences
CRISAM - Inria Sophia Antipolis - Méditerranée
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a generation by generation approach. Then, making use of the link between the survival probability and the principal eigenvalue established in a previous work, we deduce the variations of the eigenvalue with respect to the parameter of the model.
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Contributor : Coralie Fritsch <>
Submitted on : Monday, January 23, 2017 - 2:14:46 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:31 PM
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Fabien Campillo, Nicolas Champagnat, Coralie Fritsch. On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models. Communications in Mathematical Sciences, International Press, 2017, 15 (7), pp.1801-1819. ⟨10.4310/CMS.2017.v15.n7.a1⟩. ⟨hal-01254053v3⟩

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