Swarming models with specular boundary condition and environmental noise

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 macr...

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Bibliographic Details
Published inarXiv.org
Main Authors Fetecau, Razvan C, Huang, Hui, Qiu, Jinniao
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.04.2023
Subjects
Background noise
Boundary conditions
Partial differential equations
Stochastic systems
Swarming
Tightness
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ISSN2331-8422

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Summary: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.
Bibliography:content type line 50
SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422