Quantitative Propagation of Chaos in $L^\eta (\eta \in [0,1])$-Wasserstein Distance for Mean Field Interacting Particle System

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发表日期：

2026年2月21日

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Xing Huang

摘要

In this paper, quantitative propagation of chaos in $L^\eta $ $L^{η}$ ( $\eta \in (0,1]$ $η \in (0, 1]$ )-Wasserstein distance $\mathbb {W}_\eta $ $W_{η}$ for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting. The result is new even in the case with non-interacting noise. When the diffusion coefficient is distribution free, quantitative propagation of chaos in total variation distance(i.e. 2 $\mathbb {W}_0$ $W_{0}$ ) is also established. The non-degenerate and second order system are investigated respectively and the main tool relies on the the Duhamel formula and gradient estimate of the decoupled SDEs.

Quantitative Propagation of Chaos in \(L^\eta (\eta \in [0,1])\)-Wasserstein Distance for Mean Field Interacting Particle System

摘要