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arXiv · 2407.19557

Neural stochastic Volterra equations: learning path-dependent dynamics

Martin Bergerhausen·David J. Prömel·David Scheffels
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Abstract

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, the rough Heston model and a monetary reserve dynamics, are presented, comparing the performance of neural SVEs, neural SDEs and Deep Operator Networks (DeepONets).

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Martin Bergerhausen, David J. Prömel, David Scheffels. 2024-07-28. Neural stochastic Volterra equations: learning path-dependent dynamics. https://arxiv.org/abs/2407.19557

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