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Abstract
We consider the classical Yaglom limit theorem for a branching Markov process X = (X _{t}, t ≥ 0), with nonlocal branching mechanism in the setting that the mean semigroup is critical, that is, its leading eigenvalue is zero. In particular, we show that there exists a constant c(f ) such that (Formula Presented) where e _{c(f )} is an exponential random variable with rate c(f ) and the convergence is in 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 branching Brownian motion in a bounded domain and superprocesses, (Probab. Theory Related Fields 173 (2019) 999–1062; Electron. Commun. Probab. 23 (2018) 42), these results do not allow for nonlocal branching which complicates the analysis. Our approach and the main novelty of this work is based around a precise result for the scaled asymptotics for the kth martingale moments of X (rather than the Yaglom limit itself).
Original language  English 

Pages (fromto)  2373–2408 
Number of pages  36 
Journal  Annals of Probability 
Volume  50 
Issue number  6 
Early online date  23 Oct 2022 
DOIs  
Publication status  Published  30 Nov 2022 
Bibliographical note
The SCH, AEK and MW were supported by EPSRC grant EP/P009220/1.Keywords
 Branching markov process
 Neutron transport equation
 Perron– frobenius decomposition
 Quasistationary limit
 Semigroup theory
 Yaglom limit
ASJC Scopus subject areas
 Statistics and Probability
 Statistics, Probability and Uncertainty
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Dive into the research topics of 'Yaglom limit for critical nonlocal branching Markov processes'. Together they form a unique fingerprint.Projects
 2 Finished

Mathematical Theory of Radiation Transport: Nuclear Technology Frontiers (MATHRAD) **DO NOT USE THIS ONE**
Kyprianou, A., Cox, A., Pryer, T. & Hattam, L.
Engineering and Physical Sciences Research Council
1/09/22 → 31/12/22
Project: Research council

Stochastic Analysis of the Neutron Transport Equation and Applications to Nuclear Safety
Kyprianou, A., Cox, A. & Harris, S.
Engineering and Physical Sciences Research Council
16/05/17 → 31/12/21
Project: Research council