A microscopic probabilistic description of a locally regulated population and macroscopic approximations
A microscopic probabilistic description of a locally regulated population and macroscopic approximations
复制标题
DOI：
10.1214/105051604000000882
复制
发表时间：
2004-11-01
影响因子：
1.8
通讯作者：
Méléard, S
中科院分区：
文献类型：
--
作者：
Fournier, N;Méléard, S
我们考虑一个离散模型，描述了一个局部调节的空间人口死亡率选择。Bolker和Pacala和Dieckmann，Law和Murrell平行研究了这个模型。我们首先通过增加空间依赖性来推广这个模型。然后，我们给出了一个路径描述的泊松点的措施。我们表明，不同的归一化可能会导致不同的宏观近似这个模型。第一近似是确定性的，并给出了严格意义上的数密度。第二近似是Etheridge以前研究过的超过程。最后，我们研究在特定情况下的长期行为的系统和它的确定性近似。
We consider a discrete model that describes a locally regulated spatial population with mortality selection. This model was studied in parallel by Bolker and Pacala and Dieckmann, Law and Murrell. We first generalize this model by adding spatial dependence. Then we give a pathwise description in terms of Poisson point measures. We show that different normalizations may lead to different macroscopic approximations of this model. The first approximation is deterministic and gives a rigorous sense to the number density. The second approximation is a superprocess previously studied by Etheridge. Finally, we study in specific cases the long time behavior of the system and of its deterministic approximation.