Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System

Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System

Year:    2024

Author:    Yue Li, Li Chen, Zhipeng Zhang

Communications in Mathematical Research , Vol. 40 (2024), Iss. 1 : pp. 43–63

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmr.2023-0002

Communications in Mathematical Research , Vol. 40 (2024), Iss. 1 : pp. 43–63

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Stochastic particle systems cross-diffusion system mean-field limit population dynamics.

Author Details

Yue Li

Li Chen

Zhipeng Zhang