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David Scheffels

Publications and source records attributed to David Scheffels.

5 recordsLinked to original sources
arXiv2024

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

cs.LG↗
arXiv2023

Mean-field stochastic Volterra equations

The well-posedness is established for multi-dimensional mean-field stochastic Volterra equations with Lipschitz continuous coefficients and allowing for singular kernels as well as for one-dimensional mean-field stochastic Volterra equations with H\"older continuous diffusion coefficients and sufficiently regular kernels. In these different settings, quantitative, pointwise propagation of chaos results are derived for the associated Volterra type interacting particle systems.

math.PR↗
arXiv2022

On the existence of weak solutions to stochastic Volterra equations

The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented approach is based on a newly formulated local martingale problem associated to stochastic Volterra equations.

math.PR↗
arXiv2022

Stochastic Volterra equations with H\"older diffusion coefficients

The existence of strong solutions and pathwise uniqueness are established for one-dimensional stochastic Volterra equations with locally H{\"o}lder continuous diffusion coefficients and sufficiently regular kernels. Moreover, we study the sample path regularity, the integrability and the semimartingale property of solutions to one-dimensional stochastic Volterra equations.

math.PR↗