发表机构
University of Southern California; School of Science and Engineering, the Chinese University of Hong Kong (Shenzhen)（南加州大学; 香港中文大学（深圳）理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对Itô过程经验路径律，建立了(log N)^{-1/2}的Sharp Wasserstein收敛速率，采用自适应随机时间区间划分方法，其结果可应用于路径依赖SDE及McKean-Vlasov粒子系统相关估计。
AI 中文摘要
我们针对N个独立连续Itô过程副本的经验律与其共同路径律之间、由上确界范数诱导的期望p-Wasserstein距离，建立了Sharp对数阶(log N)^{-1/2}。仅假设初始条件、漂移项与扩散项被某个ρ>p≥1对应的有限ρ-矩的时间一致随机上界所控制。在此假设下，我们采用自适应随机时间区间划分方法，得到了(log n)^{-1/2}的函数量化速率。随后，利用通用转移原理将量化估计转化为等权重经验律的均值估计与非渐近偏差界。应用包括路径依赖SDE的经验路径律估计，以及路径依赖McKean-Vlasov相互作用粒子系统的路径空间混沌传播估计。
英文摘要
We establish functional quantization and empirical Wasserstein rates for continuous Itô processes under the supremum norm. We assume that the initial condition and the drift and diffusion integrands are controlled by a time-uniform random upper bound with a finite $ρ$-moment for some $ρ>1$. Under this assumption, the $n$-point $L^q$ quantization error is at most $C(\log n)^{-1/2}$ for every $1\leq q<ρ$. The known Brownian lower bound shows that the exponent $1/2$ is optimal over this class. Our proof combines an adaptive dyadic time partition with localization according to the size of the integrands. A general transfer principle yields the sharp mean rate $(\log N)^{-1/2}$ for the $p$-Wasserstein distance between the empirical law of $N$ independent copies and their common path law, together with nonasymptotic deviation bounds, whenever $1\leq p<ρ$. Applications include empirical path-law estimates for path-dependent SDEs and a path-space limit-theory estimate for path-dependent McKean--Vlasov interacting particle systems with common noise.
