@Article{CMR-40-1,
author = {Yue, Li and Li, Chen and Zhipeng, Zhang},
title = {Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System},
journal = {Communications in Mathematical Research },
year = {2024},
volume = {40},
number = {1},
pages = {43--63},
abstract = {<p style="text-align: justify;">In this paper, we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.
The convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential, where the mollification is of algebraic scaling. The main idea of the proof is to study the time
evolution of a stopped process and obtain a Grönwall type estimate by using
Taylor’s expansion around the limiting stochastic process.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2023-0002},
url = {https://global-sci.com/article/81444/convergence-towards-the-population-cross-diffusion-system-from-stochastic-many-particle-system}
}