More on the asymptotic behaviour of moments of branching Markov processes

Christopher B. C. Dean; Emma Horton

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arXiv · 2501.19268

More on the asymptotic behaviour of moments of branching Markov processes

Christopher B. C. Dean·Emma Horton

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Abstract

Consider a branching Markov process, $X = (X(t), t \ge 0)$, with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attention in the literature [6, 7] due to the importance of these results in understanding the underlying genealogical structure of $X$. In this article, we generalise the results of [7] to allow for a non-simple leading eigenvalue and to also study the higher order fluctuations of the moments of $X$. These results will be useful for proving central limit theorems and extending well-known LLN results.

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Christopher B. C. Dean, Emma Horton. 2025-01-31. More on the asymptotic behaviour of moments of branching Markov processes. https://arxiv.org/abs/2501.19268

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