On McKean-Vlasov Branching Diffusion Processes
Probability
2024-09-12 v2
Abstract
We study a nonlinear branching diffusion process in the sense of McKean, i.e., where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness result by using contraction arguments. Then we consider the notion of weak solution and its equivalent martingale problem formulation. In this setting, we provide a general weak existence result, as well as a propagation of chaos property, i.e., the McKean-Vlasov branching diffusion is the limit of a large population branching diffusion process with mean-field interaction.
Cite
@article{arxiv.2404.12964,
title = {On McKean-Vlasov Branching Diffusion Processes},
author = {Julien Claisse and Jiazhi Kang and Xiaolu Tan},
journal= {arXiv preprint arXiv:2404.12964},
year = {2024}
}