Swarming models with specular boundary condition and environmental noise
Abstract
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common environmental noise. We rigorously derive its corresponding macroscopic mean-field equation, which is a new type of stochastic partial differential equation due to the presence of common noise. The approach relies on a compactness argument, in which we first establish the tightness of the empirical measures associated with the particle system and then demonstrate that the time marginal of the limit measure is a solution to the mean-field equation.
Keywords
Cite
@article{arxiv.2304.02130,
title = {Swarming models with specular boundary condition and environmental noise},
author = {Razvan C. Fetecau and Hui Huang and Jinniao Qiu},
journal= {arXiv preprint arXiv:2304.02130},
year = {2025}
}
Comments
The conclusions from equations (4.5) to (4.7) are incorrect, since we do not know if the limit process is continuous or not