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math.PR2025
Krylov-Veretennikov decomposition for measure-valued processes induced by SDEs with interaction on Riemannian manifolds
Andrey Dorogovtsev, Alexander Weiß
We introduce a framework for stochastic differential equations (SDEs) with interaction on compact, connected, -dimensional manifolds. For SDEs whose drift and diffusion coeffici…
math.PR2025
Strong Feller Regularisation of 1-d Nonlinear Transport by Reflected Ornstein-Uhlenbeck Noise
Max-K. von Renesse, Feng-Yu Wang, Alexander Weiß
We consider equations of nonlinear transport on the circle with regular self interactions appearing in aggregation models and deterministic mean field dynamics. We introduce a rand…
math.PR2023
Intermittency Phenomena for Mass Distributions of Stochastic Flows with Interaction
Andrey Dorogovtsev, Alexander Weiß
The intermittency phenomenon is the occurrence of very high but rare peaks, which despite their rarity influence the asymptotic behaviour of the underlying system. Mathematically t…