Simon C. Harris
Many-to-few for non-local branching Markov process
Harris, Simon C.; Horton, Emma; Kyprianou, Andreas E.; Powell, Ellen
Authors
Abstract
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.
Citation
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. https://doi.org/10.1214/24-ejp1098
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 |
Electronic ISSN | 1083-6489 |
Publisher | Institute of Mathematical Statistics |
Peer Reviewed | Peer Reviewed |
Volume | 29 |
Article Number | 41 |
Pages | 1-26 |
DOI | https://doi.org/10.1214/24-ejp1098 |
Public URL | https://durham-repository.worktribe.com/output/2466682 |
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Publisher Licence URL
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Copyright Statement
Creative Commons Attribution 4.0 International License.
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