Weak and strong mean-field limits for stochastic Cucker-Smale particle systems
Résumé
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 regarding the tightness of random measures in Wasserstein spaces, we are able to construct a weak solution of the corresponding limiting SPDE. This weak convergence can be turned into a strong L^p(Ω) convergence in a setup where the diffusion coefficient on the environmental noise is bounded. The systems considered include perturbations of the Cucker-Smale model for collective motion.
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