论文标题
奇异相互作用粒子系统及其平均场限制的路径正规化
Pathwise Regularisation of Singular Interacting Particle Systems and their Mean Field Limits
论文作者
论文摘要
我们研究了平均场缩放下的单数相互作用粒子系统中噪声对某些扰动的正则化效果。特别是，我们表明，在相互作用内核上非常广泛的假设下，添加适当的不规则路径可以使这些动态定向，并恢复McKean-Vlasov限制；仅要求将其控制在可能的分配空间中。在粒子系统中，我们包括两个随机性的来源，一个常规的噪声路径$ z $，它规范动力学和一个特质噪声，我们只假定它们会在平均场缩放中收敛到McKean-vlasov方程中的代表性噪声。
We investigate the regularizing effect of certain perturbations by noise in singular interacting particle systems under the mean field scaling. In particular, we show that the addition of a suitably irregular path can regularise these dynamics and we recover the McKean--Vlasov limit under very broad assumptions on the interaction kernel; only requiring it to be controlled in a possibly distributional Besov space. In the particle system we include two sources of randomness, a common noise path $Z$ which regularises the dynamics and a family of idiosyncratic noises, which we only assume to converge in mean field scaling to a representative noise in the McKean--Vlasov equation.
