5 papers · 1 filter
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,…
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…
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…