Weak and strong mean-field limits for stochastic Cucker-Smale particle systems

2019/05/07 by Angelo Rosello, Rosello, Angelo
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1905.02499

openalex publication_date 2019/05/07 · arxiv created 2020/07/24 · arxiv updated 2020/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a particle system with a mean-field-type interaction perturbed by some common and individual noises. When the interacting kernels are sublinear and only locally Lipschitz-continuous, relying on arguments based on the tightness of random measures in Wasserstein spaces, we are able to construct a weak solution of the corresponding limiting SPDE. In a setup where the diffusion coefficient on the environmental noise is bounded, this weak convergence can be turned into a strong L^p(Ω) convergence and the propagation of chaos for the particle system can be established. The systems considered include perturbations of the Cucker-Smale model for collective motion.

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