 A generalised spatial branching process with ancestral branching to model the growth of a filamentous fungusLena Kuwata Stochastic Processes and their Applications, 2026, vol. 192, issue C Abstract: In this work, we introduce a spatial branching process to model the growth of the mycelial network of a filamentous fungus. In this model, each filament is described by the position of its tip, the trajectory of which is solution to a stochastic differential equation with a drift term which depends on all the other trajectories. Each filament can branch either at its tip or along its length, that is to say at some past position of its tip, at some time- and space-dependent rates. It can stop growing at some rate which also depends on the positions of the other tips. We first construct the measure-valued process corresponding to this dynamics, then we study its large population limit and we characterise the limiting process as the weak solution to a system of partial differential equations. Keywords: Spatial birth–death process; Historical process; Historical branching; Interacting particle systems; Large population limit (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002613 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2025.104817 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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