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Volume 40, Issue 1
Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System

Yue Li, Li Chen & Zhipeng Zhang

DOI: 10.4208/cmr.2023-0002

Commun. Math. Res., 40 (2024), pp. 43-63.

Published online: 2023-12

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35Q92, 35K45, 60J70, 82C22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-43, author = {Li , YueChen , Li and Zhang , Zhipeng}, title = {Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {40}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0002}, url = {http://global-sci.org/intro/article_detail/cmr/22281.html} }
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 -

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.

Li , YueChen , Li and Zhang , Zhipeng. (2023). Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System. Communications in Mathematical Research . 40 (1). 43-63. doi:10.4208/cmr.2023-0002
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