空间Logistic模型的动力学：有限系统
Dynamics of spatial logistic model: finite systems
摘要：
空间逻辑模型是$\mathbb{R}^d$中的点实体（粒子）系统，这些点实体（粒子）在远处的点处复制（扩散）并死亡，这也是由于竞争。这类系统的状态是所有局部有限粒子组态空间上的概率测度。在本文中，我们得到的“有限系统”的状态的演变，即在初态是由有限配置空间的子集上支持的情况下。得到的演化作为相应的Fokker-Planck方程的整体解决方案的措施支持的有限配置的集合上的空间。我们还证明了这种发展保持指数矩的存在性和绝对连续性的Lebesgue-Poisson措施。
英文摘要：
The spatial logistic model is a system of point entities (particles) in $\mathbb{R}^d$ which reproduce themselves at distant points (dispersal) and die, also due to competition. The states of such systems are probability measures on the space of all locally finite particle configurations. In this paper, we obtain the evolution of states of `finite systems', that is, in the case where the initial state is supported on the subset of the configuration space consisting of finite configurations. The evolution is obtained as the global solution of the corresponding Fokker-Planck equation in the space of measures supported on the set of finite configurations. We also prove that this evolution preserves the existence of exponential moments and the absolute continuity with respect to the Lebesgue-Poisson measure.
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