Abstract
We consider a continuous-time branching random walk in the inhomogeneous breeding potential β | ⋅ | p, where β > 0, p ≥ 0. We prove that the population almost surely explodes in finite time if p > 1 and doesn’t explode if p ≤ 1. In the non-explosive cases, we determine the asymptotic behaviour of the rightmost particle.
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Bocharov, S., Harris, S.C. (2014). Branching Random Walk in an Inhomogeneous Breeding Potential. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVI. Lecture Notes in Mathematics(), vol 2123. Springer, Cham. https://doi.org/10.1007/978-3-319-11970-0_1
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DOI: https://doi.org/10.1007/978-3-319-11970-0_1
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