Education

Publications and accepted preprints

• Becker, S., Braunwarth, R., Hutzenthaler, M., Jentzen, A., von Wurstemberger, P., Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. Commun. Comput. Phys. 28 (2020). [arXiv].
• Hutzenthaler, M., Jentzen, A., von Wurstemberger, P., Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. Electron. J. Probab. 25 (2020). [arXiv].
• Grohs, P., Hornung, F., Jentzen, A., von Wurstemberger, P., A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. [arXiv] (2018), 124 pages. To appear in the Mem. Amer. Math. Soc.
• Hutzenthaler, M., Jentzen, A., Kruse, T., Nguyen, T. A., von Wurstemberger, P., Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Proc. R. Soc. A 476 (2020). [arXiv].
• Jentzen, A., von Wurstemberger, P., Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates. J. Complexity 57 (2020). [arXiv].
• Jentzen, A., Kuckuck, B., Neufeld, A., von Wurstemberger, P., Strong error analysis for stochastic gradient descent optimization algorithms. IMA J. Numer. Anal. (2020). [arXiv].

Preprints

• Beneventano, P., Cheridito, P., Jentzen, A., von Wurstemberger, P., High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations. [arXiv] (2020), 32 pages.