2026/07/31 by Ouerdia Arezki, Paul-Marie Grollemund, Ali Zemouche
Engineering · Computer Science · Mathematics · Biochemistry, Genetics and Molecular Biology · #eess.SY #cs.SY #math.PR #q-bio.PE
arxiv created 2026/07/31 · arxiv updated 2026/08/03
In this paper, we construct a Fleming-Viot particle system for a class of subcritical Bellman-Harris processes. We prove that it selects the Yaglom limit at a polynomial rate in the number of particles. Since lifetimes are non-exponential, the population size is not Markov, and the analysis must therefore be carried out on the space of age configurations. In this setting, the Lyapunov functions used for Galton-Watson processes are no longer norm-like. Nevertheless, we establish a Yaglom theorem that strengthens the classical result: the conditional laws converge in total variation at an exponential rate, with decay rate given by the Malthusian parameter. We also prove that the drift condition, which links the hazard rate to the offspring law, is necessary within a natural class of Lyapunov functions, showing that it is a feature of the measure-valued lift rather than a defect of the estimates. Finally, we illustrate the estimator through an application to livestock epidemic surveillance, where the Yaglom limit is the null distribution of a change-detection test.