Philippe von Wurstemberger
Philippe von Wurstemberger
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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
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
M Hutzenthaler, A Jentzen, T Kruse, T Anh Nguyen, P von Wurstemberger
Proceedings of the Royal Society A 476 (2244), 20190630, 2020
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
M Hutzenthaler, A Jentzen, W Wurstemberger
Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates
A Jentzen, P Von Wurstemberger
Journal of Complexity 57, 101438, 2020
Strong error analysis for stochastic gradient descent optimization algorithms
A Jentzen, B Kuckuck, A Neufeld, P von Wurstemberger
IMA Journal of Numerical Analysis 41 (1), 455-492, 2021
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations
S Becker, R Braunwarth, M Hutzenthaler, A Jentzen, ...
arXiv preprint arXiv:2005.10206, 2020
Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing
S Becker, A Jentzen, MS Müller, P von Wurstemberger
Mathematical Finance 34 (1), 90-150, 2024
High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations
P Beneventano, P Cheridito, A Jentzen, P von Wurstemberger
arXiv preprint arXiv:2012.04326, 2020
Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
A Jentzen, B Kuckuck, P von Wurstemberger
arXiv preprint arXiv:2310.20360, 2023
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
A Jentzen, A Riekert, P von Wurstemberger
arXiv preprint arXiv:2302.03286, 2023
Overcoming the course of dimensionality with DNNs: Theoretical approximation results for PDEs
P von Wurstemberger
3rd International Conference on Computational Finance (ICCF2019), 86, 2019
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