On multitype Branching Processes with Interaction
Probability
2022-11-28 v2
Abstract
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 L\'evy processes.
Cite
@article{arxiv.2203.09701,
title = {On multitype Branching Processes with Interaction},
author = {Maria Clara Fittipaldi and Sandra Palau},
journal= {arXiv preprint arXiv:2203.09701},
year = {2022}
}