Neural stochastic Volterra equations: learning path-dependent dynamics
<|reference_start|>Neural stochastic Volterra equations: learning path-dependent dynamics: Stochastic Volterra equations (SVEs) serve as mathematical models for the time evolutions of random systems with memory effects and irregular behaviour. We introduce neural stochastic Volterra equations as a physics-inspired architecture, generalizing the class of neural stochastic differential equations, and provide some theoretical foundation. Numerical experiments on various SVEs, like the disturbed pendulum equation, the generalized Ornstein--Uhlenbeck process and the rough Heston model are presented, comparing the performance of neural SVEs, neural SDEs and Deep Operator Networks (DeepONets).<|reference_end|>
@article{prömel2024neural,
    title={Neural stochastic Volterra equations: learning path-dependent dynamics},
    author={David J. Pr"omel, David Scheffels},
    journal={arXiv preprint arXiv:2407.19557},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.19557},
    primaryClass={cs.LG math.PR stat.ML}
}