一种带有祖先分支的通用空间分支过程用于建模丝状真菌的生长
A generalised spatial branching process with ancestral branching to model the growth of a filamentous fungus
AI总结：
本文提出了一种通用的空间分支过程，通过引入祖先分支机制来建模丝状真菌菌丝网络的生长，并通过偏微分方程系统描述其大种群极限。
摘要：
在本工作中，我们引入了一个空间分支过程来建模丝状真菌菌丝网络的生长。在该模型中，每个菌丝由其尖端的位置描述，其轨迹是满足一个带有漂移项的随机微分方程的解，该漂移项依赖于所有其他轨迹。每个菌丝可以在其尖端或沿其长度分支，即在某些过去位置的尖端上，以时间与空间依赖的速率进行。它也可以以某个速率停止生长，该速率也依赖于其他尖端的位置。我们首先构造了对应于这种动态的测度值过程，然后研究了其大种群极限，并将极限过程表征为偏微分方程系统弱解。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
