A cylindrical neural approximation theorem for conditional laws of McKean-Vlasov equations with common noise

arXiv:2608.08040 · math.PR, cs.LG · Submitted 2026-08-08 · Read on arXiv

Nacira Agram, Reda Hmioui, Jan Rems

math.PR, cs.LG

Submitted: 2026-08-08

Updated: 2026-08-11

Comments: 32 pages, 7 figures, 4 tables. Code available at https://github.com/HmiouiReda/cylindrical-mckean-vlasov

Code: https://github.com/HmiouiReda/cylindrical-mckean-vlasov

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Benchmark — 24× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Consistency — 4× in this paper · explained in 3 episodes
• Composition — 2× in this paper · explained in 2 episodes
• Wasserstein Distance — 2× in this paper · explained in 6 episodes
• Adam — 1× in this paper · explained in 3 episodes
• Augmentation — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Hyperparameters — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Robustness — 1× in this paper · explained in 6 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes

Sources

• Nonlinear rough Fokker-Planck equations
• McKean-Vlasov equations with rough common noise
• Controlled rough SDEs, pathwise stochastic control and dynamic programming principles
• Deep Signature Approach for McKean-Vlasov FBSDEs in a Random Environment

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