带变异的分枝交互粒子系统和相关的极限定理

Branching interacting particle systems with mutation and related limit theorems

本文用Poisson随机测度驱动的随机积分方程构造一类带变异的分枝交互粒子系统。首先证明在某些条件下其重整化极限是同时具有局部和非局部分枝机制的超过程,其底运动是平凡的;其次证明在另外的一些条件下,其重整化极限是具有局部分枝机制和非平凡底运动的超过程。

In this paper, a class of branching particle systems with interaction and mutation are constructed as the solutions of a class of jump-type stochastic integral equations driven by some Poisson random measures. We show that, under some conditions, the scaling limit of these particle systems is a superprocess with interaction,with local and non-local branching mechanism and trivial spatial motion or with local branching mechanism and non-trivial spatial motion.