论文标题
在具有相互作用的多元分支过程中
On multitype Branching Processes with Interaction
论文作者
论文摘要
由随机Lotka-Volterra模型的激励，我们引入了离散状态相互作用的多元分支过程。我们表明，它们可以作为多维随机步行的总和，其与人口规模成正比的变化。以及与成对相互作用成正比的多维泊松过程。我们将类似的连续状态过程定义为多维SDE的独特强解决方案。我们证明，离散状态过程的缩放限制对应于其连续对应物。此外，我们表明，连续状态模型可以作为多维lévy过程的广义灯泡型转换构建。
Motivated by the stochastic Lotka-Volterra model, we introduce discrete-state interacting multitype branching processes. We show that they can be obtained as the sum of a multidimensional random walk with a Lamperti-type change proportional to the population size; and a multidimensional Poisson process with a time-change proportional to the pairwise interactions. We define the analogous continuous-state process as the unique strong solution of a multidimensional SDE. We prove that the scaling limits of the discrete-state process correspond to its continuous counterpart. In addition, we show that the continuous-state model can be constructed as a generalized Lamperti-type transformation of multidimensional Lévy processes.
