Neural stochastic Volterra equations: learning path-dependent dynamics

• URL: http://arxiv.org/abs/2407.19557v1
• Date: Sun, 28 Jul 2024 18:44:49 GMT
• Title: Neural stochastic Volterra equations: learning path-dependent dynamics
• Authors: David J. Prömel, David Scheffels,
• Abstract summary: Volterra equations (SVEs) serve as mathematical models for the time evolutions of random systems with memory effects and irregular behaviour. We introduce neural Volterra equations as a physics-inspired architecture, generalizing the class of neural 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 and the rough Heston model are presented, comparing the performance of neural SVEs, neural SDEs and Deep Operator Networks (DeepONets).

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