7 papers
Stochastic Modelling of Telomere Length Dynamics During Hematopoiesis
Sophie Baland, Simon Toupance, Denis Villemonais
We introduce a new stochastic model of telomere length dynamics during hematopoiesis. The numerous cell divisions occurring in this setting makes telomere length dynamics, and in p…
Convergence of weighted branching processes
Denis Villemonais, Nicolas Zalduendo
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infini…
Linear and uniform in time bound for the binary branching model with Moran type interactions
A M G Cox, E Horton, D Villemonais
In this note, we recall the definition of the binary branching model with Moran type interactions (BBMMI) introduced in [8]. In this interacting particle system, particles evolve,…
Stochastic branching models for the telomeres dynamics in a model including telomerase activity
Athanase Benetos, Coralie Fritsch, Emma Horton +3
Telomeres are repetitive sequences of nucleotides at the end of chromosomes, whose evolution over time is intrinsically related to biological ageing. In most cells, with each cell…
Quasi-limiting behaviour of the sub-critical Multitype Bisexual Galton-Watson Branching Process
Coralie Fritsch, Denis Villemonais, Nicolás Zalduendo
We investigate the quasi-limiting behaviour of bisexual subcritical Galton-Watson branching processes. While classical subcritical Galton-Watson processes have been extensively ana…
A branching model for intergenerational telomere length dynamics
Athanasios Benetos, Olivier Coudray, Anne Gégout-Petit +3
We build and study an individual based model of the telomere length's evolution in a population across multiple generations. This model is a continuous time typed branching process…
Stochastic Methods for Neutron Transport Equation III: Generational many-to-one and
A. M. G. Cox, E. L. Horton, A. E. Kyprianou +1
The Neutron Transport Equation (NTE) describes the flux of neutrons over time through an inhomogeneous fissile medium. In the recent articles [5, 10], a probabilistic solution of t…