Wong--Zakai Convergence and FNO Learning for Stochastic Volterra Equations
This paper studies Wong--Zakai convergence and Fourier neural operator learning for stochastic Volterra integral equations (SVIEs) describing random systems with memory. A Wong--Zakai theorem establishes convergence of pathwise solutions driven by piecewise linear approximations of Brownian motion to the corresponding SVIE solution. This convergence provides a foundation for using mirror-padded Fourier neural operators to learn the solution operator mapping initial conditions and driving noise to entire solution trajectories. Numerical experiments demonstrate competitive prediction accuracy and generalization to temporal grids finer than those used for training, while assessing the influe...
| Authors | Wonjae Lee, Jiuk Jang, Hyungbin Park |
|---|---|
| Primary category | stat.ML |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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