TY - JOUR
T1 - Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System
AU - Li , Yue
AU - Chen , Li
AU - Zhang , Zhipeng
JO - Communications in Mathematical Research 
VL - 1
SP - 43
EP - 63
PY - 2023
DA - 2023/12
SN - 40
DO - http://doi.org/10.4208/cmr.2023-0002
UR - https://global-sci.org/intro/article_detail/cmr/22281.html
KW - Stochastic particle systems, cross-diffusion system, mean-field limit, population dynamics.
AB - <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>