Arnulf Jentzen

Arnulf Jentzen (born November 1983 ) is a German mathematician and university professor at the Westphalian Wilhelms University of Münster .

From 2004 Jentzen studied mathematics at the Johann Wolfgang Goethe University in Frankfurt am Main with a diploma in 2007 and a doctorate in 2009 with Peter Kloeden ( Taylor approximations for stochastic evolution equations ). He was then a temporary academic advisor at Bielefeld University and in 2011/12 he was at Princeton University with a research grant from the German Research Foundation ( DFG ) . In 2012 he became an assistant professor at ETH Zurich . In 2019 he became a professor at the University of Münster .

He deals with machine learning ( deep learning ) with application in numerical approximation of stochastic and high-dimensional partial differential equations (overcoming the curse of dimension with stochastic approximation algorithms) as well as with regularity questions of partial differential equations. His work has applications in financial mathematics, for example.

Arnulf Jentzen is a member of the editorial boards of the journals Annals of Applied Probability, Communications in Mathematical Sciences, Journal of Complexity, Journal of Mathematical Analysis and Applications, SIAM Journal on Numerical Analysis and SIAM Journal on Scientific Computing.

For 2020 he received the Felix Klein Prize .

Fonts (selection)

• Taylor expansions of solutions of stochastic partial differential equations , Arxiv 2009
• with Martin Hairer , Martin Hutzenthaler: Loss of regularity for Kolmogorov equations , Annals of Probability, Volume 43, 2015, pp. 468–527, Arxiv
• with Peter Kloeden: Numerical approximation of stochastic partial differential equations , Milan Journal of Mathematics, Volume 77, 2009, pp. 205–244
• with Peter E. Kloeden: Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space – time noise , Proceedings of the Royal Society A, Volume 465, 2009, pp. 649–667
• with Peter Kloeden: Taylor expansions of solutions of stochastic partial differential equations with additive noise , Annals of Probability, Volume 38, 2010, pp. 532–569, Arxiv
• with Peter E. Kloeden: Taylor approximation of stochastic partial differential equations , SIAM 2011
• with Peter Kloeden, Georg Winkel: Efficient simulation of nonlinear parabolic SPDEs with additive noise , Annals of Applied Probability, Volume 21, 2011, pp. 908–950, Arxiv
• with M. Hutzenthaler, PE Kloeden: Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients , Proceedings of the Royal Society A, Volume 467, 2011, pp. 1563–1576, Arxiv
• with M. Hutzenthaler, PE Kloeden: Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients , Annals of Applied Probability, Volume 22, 2012, pp. 1611–1641, Arxiv
• with M. Hutzenthaler: Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients , Memoirs of the American Mathematical Society 236, 2015, Arxiv
• with Weinan E, J. Han: Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations , Communications in Mathematics and Statistics 2017, Arxiv
• with Christian Beck u. a .: Solving stochastic differential equations and Kolmogorov equations by means of deep learning , Arxiv , 2018
• with J. Han, E Weinan : Solving high-dimensional partial differential equations using deep learning , Proc. Nat. Acad. Sciences USA, Vol. 115, 2018, pp. 8505-8510, Arxiv

Web links

• Homepage at the University of Münster

Individual evidence

1. ↑ Arnulf Jentzen in the Mathematics Genealogy Project (English)
2. ↑ Felix Klein Prize , ECM 2020. Accessed May 14, 2020. (English)