Weak and strong mean-field limits for stochastic Cucker-Smale particle systems
Weak and strong mean-field limits for stochastic Cucker-Smale particle systems
复制标题
随机 Cucker-Smale 粒子系统的弱和强平均场限制
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Angelo Rosello
中科院分区：
文献类型：
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作者：
Angelo Rosello
我们考虑一个具有平均场型相互作用的粒子系统，它被一些常见的和个别的噪声所扰动。当相互作用的核是次线性且仅局部lipschitz连续时，依靠Wasserstein空间中随机测度的紧性论证，我们能够构造相应极限SPDE的弱解。在环境噪声的扩散系数有界的情况下，这种弱收敛可以转化为强L^p（Ω）收敛，从而可以建立粒子系统的混沌传播。所考虑的系统包括集体运动的库克-小模型的扰动。
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. 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 perturba- tions of the Cucker-Smale model for collective motion.