Fabian Hornung
Title
Cited by
Cited by
Year
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
662018
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
202019
The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates
F Hornung
Journal of Evolution Equations 18 (3), 1085-1114, 2018
202018
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
152019
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
Journal of Numerical Mathematics 1 (ahead-of-print), 2020
132020
Global solutions of the nonlinear Schrödinger equation with multiplicative noise
F Hornung
PhD thesis, Karlsruhe Institute of Technology, 2018
82018
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 8 …, 2020
72020
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
62018
Space-time deep neural network approximations for high-dimensional partial differential equations
F Hornung, A Jentzen, D Salimova
arXiv preprint arXiv:2006.02199, 2020
12020
Weak martingale solutions for the stochastic nonlinear Schrödinger equation driven by pure jump noise
Z Brzezniak, F Hornung, U Manna
12018
The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds
F Hornung
Nonlinear Differential Equations and Applications NoDEA 27 (4), 1-46, 2020
2020
The stochastic nonlinear Schr\" odinger equation in unbounded domains and manifolds
F Hornung
arXiv preprint arXiv:1906.08638, 2019
2019
MARTINGALE SOLUTIONS FOR THE STOCHASTIC NONLINEAR SCHR ODINGER EQUATION IN THE ENERGY SPACE
ZB ZNIAK, F HORNUNG, L WEIS
emu (t) 1000, 1, 2017
2017
The system can't perform the operation now. Try again later.
Articles 1–13