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19992022
most citedSolving high-dimensional partial differential equations using deep learning

1.8k citations

Showing 2016 · math.PRShow all

5 papers · 2 filters

math.PR2016★ 12 cited

On the mild Itô formula in Banach spaces

Sonja Cox, Arnulf Jentzen, Ryan Kurniawan +1

The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \& Röckner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appear in the Trans.\ Amer.\ Math…

math.PR2016★ 2 cited

On the differentiability of solutions of stochastic evolution equations with respect to their initial values

Adam Andersson, Arnulf Jentzen, Ryan Kurniawan +1

In this article we study the differentiability of solutions of parabolic semilinear stochastic evolution equations (SEEs) with respect to their initial values. We prove that if the…

math.PR2016★ 15 cited

Exponential moments for numerical approximations of stochastic partial differential equations

Arnulf Jentzen, Primož Pušnik

Stochastic partial differential equations (SPDEs) have become a crucial ingredient in a number of models from economics and the natural sciences. Many SPDEs that appear in such app…

math.PR2016★ 30 cited

Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations

Martin Hutzenthaler, Arnulf Jentzen, Diyora Salimova

This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white n…

math.PR2016★ 13 cited

Numerical analysis of lognormal diffusions on the sphere

Lukas Herrmann, Annika Lang, Christoph Schwab

Numerical solutions of stationary diffusion equations on the unit sphere with isotropic lognormal diffusion coefficients are considered. Hölder regularity in sense for isotro…