2018/02/16 by Ismaël Bailleul, Bailleul, I., Rémi Catellier +3
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Stochastic processes and financial applications #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1802.05882
openalex publication_date 2018/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide in this work a robust solution theory for random rough differential equations of mean field type dXt = V(Xt,L(Xt))dt + F(Xt,L(Xt))dWt, where W is a random rough path and L(Xt) stands for the law of Xt, with mean field interaction in both the drift and diffusivity. The analysis requires the introduction of a new rough path-like setting and an associated notion of controlled path. We use crucially Lions' approach to differential calculus on Wasserstein space along the way.