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20032023
most citedIsotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations

142 citations · 696 across the 46 of their papers we have counts for

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Showing 2018Show all

2 papers · 1 filter

math.FA2018★ 97 cited

DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing

Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen +1

We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReL…

math.NA2018

Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification

Josef Dick, Michael Feischl, Christoph Schwab

We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows…