Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs with infinite activity

2 code implementations • 8 May 2024 • Ariel Neufeld, Philipp Schmocker, Sizhou Wu

In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks suitable to approximately solve both high-dimensional nonlinear parabolic PDEs and PIDEs with jumps having (possibly) infinite activity.

Universal Approximation Property of Random Neural Networks

1 code implementation • 13 Dec 2023 • Ariel Neufeld, Philipp Schmocker

In this paper, we study random neural networks which are single-hidden-layer feedforward neural networks whose weights and biases are randomly initialized.

Global universal approximation of functional input maps on weighted spaces

1 code implementation • 5 Jun 2023 • Christa Cuchiero, Philipp Schmocker, Josef Teichmann

This then applies in particular to approximation of (non-anticipative) path space functionals via functional input neural networks.

Gaussian Processes regression +1

Chaotic Hedging with Iterated Integrals and Neural Networks

no code implementations • 21 Sep 2022 • Ariel Neufeld, Philipp Schmocker

In this paper, we extend the Wiener-Ito chaos decomposition to the class of diffusion processes, whose drift and diffusion coefficient are of linear growth.