Yaglom limit for critical neutron transport
Résumé
We consider the classical Yaglom limit theorem for the Neutron Branching Process (NBP) in the setting that the mean semigroup is critical, i.e. its leading eigenvalue is zero. We show that the law of the process conditioned on survival is asymptotically equivalent to an exponential distribution. As part of the proof, we also show that the probability of survival decays inversely proportionally to time. Although Yaglom limit theorems have recently been handled in the setting of spatial branching processes and superprocesses, as well as in the setting of isotropic homogeneous Neutron Branching Processes, our approach and the main novelty of this work is based around a precise result for the scaled asymptotics for the k-th martingale moments of the NBP (rather than the Yaglom limit itself). Our proof of the asymptotic martingale moments turns out to offer a general approach to asymptotic martingale moments of critical branching Markov processes with a non-local branching mechanism. Indeed this is the context in which we give both our moment proofs and the Yaglom limit.
Origine : Fichiers produits par l'(les) auteur(s)