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Many-to-few for non-local branching Markov process

Harris, Simon C.; Horton, Emma; Kyprianou, Andreas E.; Powell, Ellen

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Simon C. Harris

Emma Horton

Andreas E. Kyprianou


We provide a many-to-few formula in the general setting of non-local branching Markov processes. This formula allows one to compute expectations of k-fold sums over functions of the population at k different times. The result generalises [13] to the non-local setting, as introduced in [11] and [8]. As an application, we consider the case when the branching process is critical, and conditioned to survive for a large time. In this setting, we prove a general formula for the limiting law of the death time of the most recent common ancestor of two particles selected uniformly from the population at two different times, as t→∞. Moreover, we describe the limiting law of the population sizes at two different times, in the same asymptotic regime.


Harris, S. C., Horton, E., Kyprianou, A. E., & Powell, E. (2024). Many-to-few for non-local branching Markov process. Electronic Journal of Probability, 29, 1-26.

Journal Article Type Article
Acceptance Date Feb 9, 2024
Online Publication Date Mar 4, 2024
Publication Date 2024
Deposit Date May 28, 2024
Publicly Available Date May 28, 2024
Journal Electronic Journal of Probability
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 29
Article Number 41
Pages 1-26
Public URL


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