A cylindrical neural approximation theorem for conditional laws of McKean-Vlasov equations with common noise
We introduce conditional cylindrical neural networks for approximating functionals of conditional laws in McKean-Vlasov equations with common noise. Fourier moments of the initial law and truncated signatures of the time augmented common noise are mapped by a mixture density network to a Gaussian mixture approximation of the conditional law. A cylindrical neural network then evaluates the target functional through analytic integrals against this predicted measure. Rough path well posedness and stability provide a conditional law map that is continuous in the initial distribution and the rough driver and agrees almost surely with the classical conditional law at the Itô Brownian lift. Comb...
| Authors | Nacira Agram, Reda Hmioui, Jan Rems |
|---|---|
| Primary category | math.PR |
| Published | 8 August 2026 |
| Last updated at source | 8 August 2026 |
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