Many-to-few for non-local branching Markov process
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Publication:6126962
DOI10.1214/24-EJP1098arXiv2211.08662OpenAlexW4315709875MaRDI QIDQ6126962
Author name not available (Why is that?)
Publication date: 10 April 2024
Published in: (Search for Journal in Brave)
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 [14] 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 tends to infinity. Moreover, we describe the limiting law of the population sizes at two different times, in the same asymptotic regime.
Full work available at URL: https://arxiv.org/abs/2211.08662
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