Fabian Hornung
TitleCited byYear
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
P Grohs, F Hornung, A Jentzen, P Von Wurstemberger
arXiv preprint arXiv:1809.02362, 2018
242018
Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space
Z Brzeźniak, F Hornung, L Weis
Probability Theory and Related Fields 174 (3-4), 1273-1338, 2019
122019
The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates
F Hornung
Journal of Evolution Equations 18 (3), 1085-1114, 2018
122018
Weak martingale solutions for the stochastic nonlinear Schrödinger equation driven by pure jump noise
Z Brzeźniak, F Hornung, U Manna
Stochastics and Partial Differential Equations: Analysis and Computations, 1-53, 2019
62019
Uniqueness of martingale solutions for the stochastic nonlinear Schr\" odinger equation on 3d compact manifolds
Z Brzezniak, F Hornung, L Weis
arXiv preprint arXiv:1808.10619, 2018
42018
Global solutions of the nonlinear Schrödinger equation with multiplicative noise
F Hornung
PhD thesis, Karlsruhe Institute of Technology, 2018
42018
Space-time error estimates for deep neural network approximations for differential equations
P Grohs, F Hornung, A Jentzen, P Zimmermann
arXiv preprint arXiv:1908.03833, 2019
2019
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard …
C Beck, F Hornung, M Hutzenthaler, A Jentzen, T Kruse
arXiv preprint arXiv:1907.06729, 2019
2019
The stochastic nonlinear Schr\" odinger equation in unbounded domains and manifolds
F Hornung
arXiv preprint arXiv:1906.08638, 2019
2019
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Articles 1–9