Work

Long-time behaviour of a multidimensional age-dependent branching process with a singular jump kernel modelling telomere shortening

Year: 2026

Type: article

Abstract: In this article, we investigate the ergodic behaviour of a multidimensional age-dependent branching process with a singular jump kernel, motivated by studying the phenomenon of telomere shortening in cell populations. Our model tracks individuals evolving within a continuous-time framework indexed by a binary tree, characterised by age and a multidimensional trait. Branching events occur with rates dependent on age, where offspring inherit traits from their parent with random increase or decrease in some coordinates, while the most of them are left unchanged. Exponential ergodicity is obtained at the cost of an exponential normalisation, despite the fact that we have an unbounded age-dependent birth rate that may depend on the multidimensional trait, and a non-compact transition kernel. These two difficulties are respectively treated by stochastically comparing our model to Bellman-Harris processes, and by using a weak form of a Harnack inequality. We also provide two examples motivated by our biological context in which the assumptions of our main result are verified.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1469

Authors: Jules Olayé, Milica Tomašević