论文标题
具有Moran类型相互作用的二进制分支过程
Binary branching processes with Moran type interactions
论文作者
论文摘要
本文的目的是研究具有MORAN类型相互作用的二元分支粒子系统的较大种群限制：我们引入了一个新模型，颗粒可以独立发展，再现和死亡，并且可能取决于整个系统的配置，粒子的死亡可能会触发另一个粒子事件的复制，而分支事件可能会触发另一个粒子的死亡。我们研究了新模型的职业度量，将其明确与基础马尔可夫进化的Feynman-Kac半群有关，并量化了其正常化之间的L2距离。该模型扩展了[18、19、6、7、57]中讨论的固定尺寸的Moran类型相互作用的粒子系统，我们确实将证明我们的模型在用于近似出生和死亡过程的情况下优于后者。我们讨论了模型的其他几种应用，包括中子传输方程[36，15]和人口大小动态。
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that may depend on the configuration of the whole system, the death of a particle may trigger the reproduction of another particle, while a branching event may trigger the death of an other one. We study the occupation measure of the new model, explicitly relating it to the Feynman-Kac semigroup of the underlying Markov evolution and quantifying the L2 distance between their normalisations. This model extends the fixed size Moran type interacting particle system discussed in [18, 19, 6, 7, 57] and we will indeed show that our model outperforms the latter when used to approximate a birth and death process. We discuss several other applications of our model including the neutron transport equation [36, 15] and population size dynamics.
