发表机构
Technische Universität Berlin; Max–Planck Institute for Mathematics in the Sciences, Leipzig; School of Mathematics, University of Edinburgh（柏林工业大学; 莱比锡马克斯·普朗克科学计量学研究所; 爱丁堡大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出转移原理，将噪声同步化从冻结扩散SDE推广至McKean--Vlasov SDE，并首次应用于集合卡尔曼采样，同时改进乘性噪声同步化准则至非紧致控制设定。
AI 中文摘要
研究了McKean--Vlasov随机微分方程的噪声同步化现象。引入了一个转移原理，通过该原理，噪声同步化和对角混合性质可以从一个相关的极限冻结扩散随机微分方程转移到真正依赖于分布的McKean--Vlasov随机微分方程。通过将其应用于集合卡尔曼采样，展示了该原理的实用性，从而提供了其在采样语境中的首次应用。随后从采样的视角重新审视了乘性噪声随机微分方程的同步化问题。现有的为噪声同步化提供充分条件的一般框架被改进并扩展到非紧致状态空间上的控制导向设定，并推导了可用于验证这些准则的系数级条件。受采样中外推方案的启发，强调了在固定采样器的耦合构造中的自由度，以及选择具有有利同步化性质的耦合的优势。
英文摘要
Synchronisation by noise for McKean--Vlasov stochastic differential equations is investigated. A transfer principle is introduced by which synchronisation by noise and diagonal mixing can be transferred from an associated limiting frozen-diffusion SDE to a genuinely law-dependent McKean--Vlasov SDE. The usefulness of this principle is demonstrated through an application to ensemble Kalman sampling, thereby providing its first application in a sampling context. Synchronisation for SDEs with multiplicative noise is then revisited from the perspective of sampling. Existing general frameworks providing sufficient conditions for synchronisation by noise are refined and extended to a control-oriented setting on noncompact state spaces, and coefficient-level conditions are derived by which these criteria can be verified. Motivated by extrapolation schemes in sampling, the freedom in the construction of couplings for a fixed sampler is emphasised, together with the advantage of choosing couplings that exhibit favourable synchronisation properties.
