Arnulf Jentzen
University of Münster The Chinese University of Hong Kong, Shenzhen
Address at the University of Münster:
Prof. Dr. Arnulf Jentzen
Institute for Analysis and Numerics
Applied Mathematics Münster
Faculty of Mathematics and Computer Science
University of Münster
Einsteinstraße 62
48149 Münster
Germany
Office: Room 120.005
Fon (Secretariat): +49 251 8333792
Fax: +49 251 8332729
Office hour: on appointment
Email: ajentzen (at) unimuenster.de
Homepage at the University of Münster: https://www.unimuenster.de/AMM/en/Jentzen/Mitarbeiter/Jentzen.shtml
Personal homepage: http://www.ajentzen.de
Born: November 1983 (age 37)
Links:
[Profile on Google Scholar]
[Profile on ResearchGate]
[Profile on MathSciNet]
[ETH Webmail]
Last update of this homepage: April 4th, 2021
Short Curriculum Vitae
2004—2007     Diploma studies in Mathematics, 
    Faculty of Computer Science and Mathematics, Goethe University Frankfurt 
2007—2009     PhD studies in Mathematics, 
    Faculty of Computer Science and Mathematics, Goethe University Frankfurt 
2009—2010     Assistant Professor (Akademischer Rat a.Z.), 
    Faculty of Mathematics, Bielefeld University 
2011—2012     Research Fellowship (German Research Foundation), 
    Program in Applied and Computational Mathematics, Princeton University 
2012—2019     Assistant Professor for Applied Mathematics, 
    Department of Mathematics, ETH Zurich 
2019—     Full Professor for Applied Mathematics, 
    Faculty of Mathematics and Computer Science, University of Münster 
2021—     Full Professor for Data Science, 
    School of Data Science, The Chinese University of Hong Kong, Shenzhen 
Research group
Current members of the research group
 Christian Beck (PhD student at DMATH, ETH Zurich, joint supervision with Prof. Dr. Norbert Hungerbühler)
 Robin Gräber (PhD Student at the Faculty of Mathematics and Computer Science, University of Muenster)
 Prof. Dr. Arnulf Jentzen (Head of the research group)
 Shokhrukh Ibragimov (PhD Student at the Faculty of Mathematics and Computer Science, University of Muenster)
 Timo Kröger (PhD Student at the Faculty of Mathematics and Computer Science, University of Muenster)
 Dr. Benno Kuckuck (Postdoc at the Faculty of Mathematics and Computer Science, University of Muenster)
 Adrian Riekert (PhD Student at the Faculty of Mathematics and Computer Science, University of Muenster)
 Florian Rossmannek (PhD student at DMATH, ETH Zurich, joint supervision with Prof. Dr. Patrick Cheridito)
 Philippe von Wurstemberger (PhD student at DMATH, ETH Zurich, joint supervision with Prof. Dr. Patrick Cheridito)
 Philipp Zimmermann (PhD student at DMATH, ETH Zurich, joint supervision with Prof. Dr. Patrick Cheridito)
Former members of the research group
 Dr. Sebastian Becker (former PhD student, joint supervision
with Prof. Dr. Peter E. Kloeden, 20102017, now Postdoc at ETH Zurich)
 Prof. Dr. Sonja Cox (former Postdoc/Fellow, 20122014, now Associate Professor at the University of Amsterdam)
 Dr. Fabian Hornung (former Postdoc/Fellow, 20182018, now at SAP)
 Prof. Dr. Raphael Kruse
(former Postdoc, 20122014, now Associate Professor at the Martin Luther University HalleWittenberg)
 Dr. Ryan Kurniawan (former PhD student, 20142018, now Associate at Market Risk Analytics at Morgan Stanley UK Ltd.)
 Prof. Dr. Ariel Neufeld (former Postdoc/Fellow, joint mentoring with Prof. Dr. Patrick Cheridito, 20182018,
now Assistant Professor at NTU Singapore)
 Dr. Primoz Pusnik (former PhD Student, 20142020, now Quantitative Developer at Vontobel)
 Dr. Diyora Salimova (former PhD student, 20152019, now Postdoc at ETH Zurich)
 Prof. Dr. Michaela Szoelgyenyi (former Postdoc/Fellow, 20172018, now Full Professor at the University of Klagenfurt)
 Dr. Timo Welti (former PhD Student, 20152020, now Data Analytics Consultant at D ONE Solutions AG)
 Dr. Larisa Yaroslavtseva
(former Postdoc, 20182018, now interim professor at the University of Ulm)
Research areas
 Machine learning (mathematics for deep learning,
stochastic gradient descent methods, deep neural networks,
empirical risk minimization)
 Stochastic analysis (stochastic calculus, wellposedness and regularity analysis for
stochastic ordinary and partial differential equations)
 Numerical analysis (computational stochastics/stochastic numerics, computational finance)
 Analysis of partial differential equations (wellposedness and regularity analysis for partial differential equations)
Current editorial boards affiliations
Past editorial boards affiliations
Preprints
 Riekert, A., Jentzen, A.,
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions.
[arXiv] (2021), 29 pages.
 Cheridito, P., Jentzen, A., Rossmannek, F.,
Landscape analysis for shallow ReLU neural networks:
complete classification of critical points for affine target functions.
[arXiv] (2021), 19 pages.
 Grohs, P., Ibragimov, S., Jentzen, A., Koppensteiner, S.,
Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality.
[arXiv] (2021), 53 pages.
 Beck, C., Hutzenthaler, M., Jentzen, A., Magnani, E.,
Full history recursive multilevel Picard approximations for ordinary differential equations with expectations.
[arXiv] (2021), 24 pages.
 Jentzen, A., Kröger, T.,
Convergence rates for gradient descent in the training of overparameterized artificial neural networks with biases.
[arXiv] (2021), 38 pages.
 Cheridito, P., Jentzen, A., Riekert, A., Rossmannek, F.,
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions.
[arXiv] (2021), 23 pages.
 Beck, C., Hutzenthaler, M., Jentzen, A., Kuckuck, B.,
An overview on deep learningbased approximation methods for partial differential equations.
[arXiv] (2020), 22 pages.
 Jentzen, A., Riekert, A.,
Strong overall error analysis for the training of artificial neural networks via random initializations.
[arXiv] (2020), 40 pages.
 Beneventano, P., Cheridito, P., Jentzen, A., von Wurstemberger, P.,
Highdimensional approximation spaces of artificial neural networks
and applications to partial differential equations.
[arXiv] (2020), 32 pages.
 Beck, C., Becker, S., Cheridito, P., Jentzen, A., Neufeld, A.,
Deep learning based numerical approximation algorithms for stochastic partial differential equations
and highdimensional nonlinear filtering problems.
[arXiv] (2020), 58 pages.
 Beck, C., Jentzen, A., Kruse, T.,
Nonlinear Monte Carlo methods with polynomial runtime for highdimensional iterated nested expectations.
[arXiv] (2020), 47 pages.
 Hutzenthaler, M., Jentzen, A., Kruse, T., Nguyen, T.,
Multilevel Picard approximations for highdimensional semilinear secondorder PDEs with Lipschitz nonlinearities.
[arXiv] (2020), 37 pages.
 E, W., Han, J., Jentzen, A.,
Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning.
[arXiv] (2020), 40 pages.
 Bercher, A., Gonon, L., Jentzen, A., Salimova, D.,
Weak error analysis for stochastic gradient descent optimization algorithms.
[arXiv] (2020), 123 pages.
 Hornung, F., Jentzen, A., Salimova, D.,
Spacetime deep neural network approximations for highdimensional partial differential equations.
[arXiv] (2020), 52 pages.
 Jentzen, A., Welti, T.,
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation.
[arXiv] (2020), 51 pages.
 Beck, C., Gonon, L., Jentzen, A.,
Overcoming the curse of dimensionality in the numerical
approximation of highdimensional semilinear elliptic partial
differential equations.
[arXiv] (2020), 50 pages.
 Jentzen, A., Kuckuck, B., MuellerGronbach, T., Yaroslavtseva, L.,
Counterexamples to local Lipschitz and local Hölder continuity
with respect to the initial values for additive noise driven SDEs with
smooth drift coefficient functions with at most polynomially growing
derivatives.
[arXiv] (2020), 27 pages.
 Giles, M. B., Jentzen, A., Welti, T.,
Generalised multilevel Picard approximations.
[arXiv] (2019), 61 pages.
 Hutzenthaler, M., Jentzen, A., Lindner, F., Pusnik, P.,
Strong convergence rates on the whole probability space for
spacetime discrete numerical approximation schemes for stochastic
Burgers equations.
[arXiv] (2019), 60 pages.
 Beck, C., Jentzen, A., Kuckuck, B.,
Full error analysis for the training of deep neural networks.
[arXiv] (2019), 43 pages.
 Grohs, P., Hornung, F., Jentzen, A., Zimmermann, P.,
Spacetime error estimates for deep neural network approximations for differential equations.
[arXiv] (2019), 86 pages.
 Beck, C., Becker, S., Cheridito, P., Jentzen, A., Neufeld, A.,
Deep splitting method for parabolic PDEs.
[arXiv] (2019), 40 pages.
 Jentzen, A., Kuckuck, B., MuellerGronbach, T., Yaroslavtseva, L.,
On the strong regularity of degenerate additive noise driven
stochastic differential equations with respect to their initial values.
[arXiv] (2019), 59 pages.
 Beccari, M., Hutzenthaler, M., Jentzen, A., Kurniawan, R., Lindner, F., Salimova, D.,
Strong and weak divergence of exponential and linearimplicit
Euler approximations for stochastic partial differential equations with
superlinearly growing nonlinearities.
[arXiv] (2019), 65 pages.
 Cox, S., Jentzen, A., Lindner, F.,
Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noise.
[arXiv] (2019), 51 pages.
 Hudde, A., Hutzenthaler, M., Jentzen, A., Mazzonetto, S.,
On the ItôAlekseevGröbner formula for stochastic differential equations.
[arXiv] (2018), 29 pages.
 Beck, C., Becker, S., Grohs, P., Jaafari, N., Jentzen, A.,
Solving stochastic differential equations and Kolmogorov equations by means of deep learning.
[arXiv] (2018), 56 pages.
 Becker, S., Gess, B., Jentzen, A., Kloeden, P. E.,
Strong convergence rates for explicit spacetime discrete numerical approximations of stochastic AllenCahn equations.
[arXiv] (2017), 104 pages.
 Hefter, M., Jentzen, A., and Kurniawan, R.,
Weak convergence rates for numerical approximations of stochastic
partial differential equations with nonlinear diffusion coefficients in
UMD Banach spaces.
[arXiv] (2016), 51 pages.
 Hutzenthaler, M., Jentzen, A. and Noll, M.,
Strong convergence rates and temporal regularity for
CoxIngersollRoss processes and Bessel processes with accessible
boundaries.
[arXiv] (2014), 32 pages.
 Hefter, M., Jentzen, A., Kurniawan, R.,
Counterexamples to regularities for the derivative processes associated to stochastic evolution equations.
[arXiv] (2017), 26 pages.
Revision requested from Stoch. Partial Differ. Equ. Anal. Comput.
Publications and accepted research articles
 Becker, S., Cheridito, P., Jentzen, A., Welti, T.,
Solving highdimensional optimal stopping problems using deep learning.
[arXiv] (2019), 42 pages.
Accepted in European Journal of Applied Mathematics.
 Jentzen, A., Lindner, F., Pusnik, P.,
Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise.
[arXiv] (2019), 54 pages.
Accepted in Nonlinear Analysis.
 Beck, C., Gonon, L., Hutzenthaler, M., Jentzen, A.,
On existence and uniqueness properties for solutions of stochastic fixed point equations.
[arXiv] (2019), 33 pages.
Accepted in DCDSB.
 Grohs, P., Jentzen, A., Salimova, D.,
Deep neural network approximations for Monte Carlo algorithms.
[arXiv] (2019), 45 pages.
Accepted in SN Partial Differential Equations and Applications.
 Beck, C., Hutzenthaler, M., Jentzen, A.,
On nonlinear FeynmanKac formulas for viscosity solutions of semilinear parabolic partial differential equations.
[arXiv] (2020), 54 pages.
Accepted in Stochastics and Dynamics.
 Becker, S., Braunwarth, R., Hutzenthaler, M., Jentzen, A., von Wurstemberger, P.,
Numerical simulations for full history recursive multilevel Picard approximations for systems of highdimensional partial differential equations.
[arXiv] (2020), 21 pages.
Accepted in Communications in Computational Physics.
 Beck, C., Hornung, F., Hutzenthaler, M., Jentzen, A., Kruse, T.,
Overcoming the curse of dimensionality in the numerical
approximation of AllenCahn partial differential equations via truncated
fullhistory recursive multilevel Picard approximations.
[arXiv] (2019), 30 pages.
Accepted in J. Numer. Math.
 Berner, J., Elbraechter, D., Grohs, P., Jentzen, A.,
Towards a regularity theory for ReLU networks  chain rule and global error estimates.
Sampling Theory and Applications 2019.
[arXiv] (2019), 5 pages.
 Elbraechter, D., Grohs, P., Jentzen, A., Schwab, C.,
DNN Expression Rate Analysis of Highdimensional PDEs: Application to Option Pricing.
[arXiv] (2018), 50 pages.
Accepted in Constr. Approx.
 Jentzen, A., Salimova, D., Welti, T.,
A proof that deep artificial neural networks overcome the curse
of dimensionality in the numerical approximation of Kolmogorov partial
differential equations with constant diffusion and nonlinear drift
coefficients.
[arXiv] (2018), 48 pages.
Accepted in Comm. Math. Sci.
 Becker, S., Cheridito, P., Jentzen, A.,
Pricing and hedging Americanstyle options with deep learning.
[arXiv] (2019), 12 pages.
Accepted in J. Risk Financial Manag.
 Cheridito, P., Jentzen, A., Rossmannek, F.,
Efficient approximation of highdimensional functions with deep neural networks.
[arXiv] (2019), 19 pages.
Accepted in IEEE Transactions on Neural Networks and Learning Systems.
 Hutzenthaler, M., Jentzen, A., Kruse, T.,
Overcoming the curse of dimensionality in the numerical
approximation of parabolic partial differential equations with
gradientdependent nonlinearities.
[arXiv] (2019), 33 pages.
Accepted in Found. Comp. Math.
 Gonon, L., Grohs, P., Jentzen, A., Kofler, D., Siska, D.,
Uniform error estimates for artificial neural network approximations
for heat equations.
[arXiv] (2019), 70 pages.
Accepted in IMA J. Num. Anal.
 Andersson, A., Jentzen, A., and Kurniawan, R.,
Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values.
[arXiv] (2015), 31 pages.
Accepted in J. Math. Anal. Appl..
 Berner, J., Grohs, P., Jentzen, A.,
Analysis of the generalization error: Empirical risk
minimization over deep artificial neural networks overcomes the curse of
dimensionality in the numerical approximation of BlackScholes partial
differential equations.
[arXiv] (2018), 35 pages.
 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.
[arXiv] (2018), 30 pages.
Accepted in Proc. Roy. Soc. A.
 E, W., Hutzenthaler, M., Jentzen, A., and Kruse, T.,
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations.
[arXiv] (2017), 18 pages.
Accepted in SN Partial Differential Equations and Applications.
 Cox, S., Hutzenthaler, M. and Jentzen, A.,
Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations.
[arXiv] (2013), 54 pages.
Accepted in Memoires of the American Mathematical Society.
 Fehrman, B., Gess, B., Jentzen, A.,
Convergence rates for the stochastic gradient descent method for nonconvex objective functions.
[arXiv] (2019), 52 pages.
Accepted in J. Mach. Learn. Res.
 Hutzenthaler, M., Jentzen, A., von Wurstemberger, P.,
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks.
[arXiv] (2019), 71 pages.
Accepted in Electronic Journal of Probability
 Jentzen, A., Lindner, F., Pusnik, P.,
Exponential moment bounds and strong convergence rates for tamedtruncated numerical approximations of stochastic convolutions.
[arXiv] (2018), 25 pages.
Accepted in Numerical Algorithms.
 Jentzen, A., Kuckuck, B., Neufeld, A., von Wurstemberger, P.,
Strong error analysis for stochastic gradient descent optimization algorithms.
[arXiv] (2018), 75 pages.
Accepted in IMA J. Num. Anal.
 Cox, S., Hutzenthaler, M., Jentzen, A., van Neerven, J., and Welti, T.,
Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions.
[arXiv] (2016), 38 pages.
Accepted in IMA J. Num. Anal.
 Jacobe de Naurois, L., Jentzen, A., and Welti, T.,
Weak convergence rates for spatial spectral Galerkin approximations
of semilinear stochastic wave equations with multiplicative noise.
[arXiv] (2015), 27 pages. Accepted in Appl. Math. Optim.
 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 BlackScholes partial differential equations.
[arXiv] (2018), 124 pages. Accepted in Mem. Amer. Math. Soc..
 Cheridito, P., Jentzen, A., Rossmannek, F.,
Nonconvergence of stochastic gradient descent in the training of deep neural networks.
[arXiv] (2020), 12 pages.
Accepted in J. Complexity.
 Becker, S., Gess, B., Jentzen, A., Kloeden, P. E.,
Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations.
BIT Numerical Mathematics ? (2020).
[arXiv].
 Hutzenthaler, M., Jentzen, A., Kruse, T., Nguyen, T. A.,
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations.
Springer Nat. Part. Diff. Equ. Appl. ? (2020).
[arXiv].
 Jentzen, A. and Kurniawan, R.,
Weak convergence rates for Eulertype approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients.
Found. Comp. Math. ? (2020).
[arXiv].
 Hutzenthaler, M. and Jentzen, A.,
On a perturbation theory and on strong convergence rates for
stochastic ordinary and partial differential equations with nonglobally
monotone coefficients.
The Annals of Probability 48 (2020), 5393.
[arXiv].
 Jentzen, A. and Pusnik, P.,
Strong convergence rates for an explicit numerical approximation
method for stochastic evolution equations with nonglobally Lipschitz
continuous nonlinearities.
IMA J. Numer. Anal. 40 (2020), 10051050.
[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), 101438.
[arXiv].
 Da Prato, G., Jentzen, A. and Röckner, M.,
A mild Ito formula for SPDEs.
Trans. Amer. Math. Soc. 372 (2019).
[arXiv].
 Beck, C., E, W., Jentzen, A.,
Machine learning approximation algorithms for highdimensional fully
nonlinear partial differential equations and secondorder backward
stochastic differential equations.
J. Nonlinear Sci. 29 (2019), 15631619.
[arXiv].
 Jentzen, A., Lindner, F., Pusnik, P.,
On the AlekseevGröbner formula in Banach spaces.
Discrete Contin. Dyn. Syst. Ser. B 24 (2019), 44754511.
[arXiv].
 Becker, S., Cheridito, P., Jentzen, A.,
Deep optimal stopping.
J. Mach. Learn. Res. 20 (2019), 125.
[arXiv].
 E, W., Hutzenthaler, M., Jentzen, A., Kruse, T.,
On multilevel Picard numerical approximations for highdimensional
nonlinear parabolic partial differential equations and highdimensional
nonlinear backward stochastic differential equations.
J. Sci. Comput. 79 (2019), 15341571.
[arXiv].
 Andersson, A., Hefter, M., Jentzen, A., and Kurniawan, R.,
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces.
Potential Analysis 50 (2019), 347379.
[arXiv].
 Conus, D., Jentzen, A. and Kurniawan, R.,
Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients.
Ann. Appl. Probab. 29 (2019), 653716.
[arXiv].
 Becker, S. and Jentzen, A.,
Strong convergence rates for nonlinearitytruncated Eulertype approximations of stochastic GinzburgLandau equations.
Stochastic Process. Appl. 129 (2018), 2869.
[arXiv].
 Hefter, M., Jentzen, A.,
On arbitrarily slow convergence rates for strong numerical
approximations of CoxIngersollRoss processes and squared Bessel
processes.
Finance Stoch. 23 (2019), 139172.
[arXiv].
 Jentzen, A., Salimova, D., Welti, T.,
Strong convergence for explicit spacetime discrete numerical approximation methods for stochastic Burgers equations.
J. Math. Anal. Appl. 469 (2019), 661704.
[arXiv].
 Hutzenthaler, M., Jentzen, A., Salimova, D.,
Strong convergence of fulldiscrete nonlinearitytruncated accelerated exponential Eulertype approximations for
stochastic KuramotoSivashinsky equations.
Comm. Math. Sci. 16 (2018), 14891529.
[arXiv].
 Cox, S., Jentzen, A., Kurniawan, R., and Pusnik, P.,
On the mild Ito formula in Banach spaces.
Discrete Contin. Dyn. Syst. Ser. B. 23 (2018), 22172243.
[arXiv].
 Jentzen, A. and Pusnik, P.,
Exponential moments for numerical approximations of stochastic partial differential equations.
SPDE: Anal. and Comp. 6 (2018), 565617.
[arXiv].
 Han, J., Jentzen, A., E, W.,
Solving highdimensional partial differential equations using deep learning.
Proc. Natl. Acad. Sci. 115 (2018), 85058510.
[arXiv].
 Jacobe de Naurois, L., Jentzen, A., and Welti, T.,
Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations.
Stochastic partial differential equations
and related fields, 237248, Springer Proc. Math. Stat., 229, Springer, Cham, 2018.
[arXiv].
 Hutzenthaler, M., Jentzen, A. and Wang, X.,
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations.
Math. Comp. 87 (2018), 13531413.
[arXiv].
 Gerencsér, M., Jentzen, A., and Salimova, D.,
On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions.
Proc. Roy. Soc. London A 473 (2017).
[arXiv].
 E, W., Han, J., Jentzen, A.,
Deep learningbased numerical methods for highdimensional
parabolic partial differential equations and backward stochastic
differential equations.
Commun. Math. Stat. 5 (2017), 349380.
[arXiv].
 Andersson, A., Jentzen, A., Kurniawan, R., and Welti, T.,
On the differentiability of solutions of stochastic evolution equations with respect to their initial values.
Nonlinear Analysis 162 (2017), 128161.
[arXiv].
 Jentzen, A., MüllerGronbach, T., and Yaroslavtseva, L.,
On stochastic differential equations with arbitrary slow convergence rates for strong approximation.
Commun. Math. Sci. 14 (2016), no. 6, 14771500.
[arXiv].
 Becker, S., Jentzen, A. and Kloeden, P. E.,
An exponential WagnerPlaten type scheme for SPDEs.
SIAM J. Numer. Anal. 54 (2016), no. 4, 23892426.
[arXiv].
 E, W., Jentzen, A. and Shen, H.,
Renormalized powers of OrnsteinUhlenbeck processes and wellposedness of stochastic GinzburgLandau equations.
Nonlinear Anal.
142 (2016), no. 142, 152193. [arXiv].
 Hutzenthaler, M. and Jentzen, A.,
Numerical approximations of stochastic differential equations with
nonglobally Lipschitz continuous coefficients.
Mem. Amer. Math. Soc.
236 (2015), no. 1112, 99 pages.
[arXiv].
 Jentzen, A. and Röckner, M.,
A Milstein scheme for SPDEs.
Found. Comput. Math.
15 (2015), no. 2, 313362.
[arXiv].
 Hairer, M., Hutzenthaler, M. and Jentzen, A.,
Loss of regularity for Kolmogorov equations.
Ann. Probab.
43 (2015), no. 2, 468527.
[arXiv].
 Hutzenthaler, M., Jentzen, A. and Kloeden, P. E.,
Divergence of the multilevel Monte Carlo Euler method for nonlinear
stochastic differential equations.
Ann. Appl. Probab. 23 (2013),
no. 5, 19131966. [arXiv].
 Blömker, D. and Jentzen, A.,
Galerkin approximations for the
stochastic Burgers equation.
SIAM J. Numer. Anal.
51 (2013), no. 1, 694715.
[arXiv].
 Hutzenthaler, M., Jentzen, A. and Kloeden, P. E.,
Strong convergence of an explicit numerical method
for SDEs with nonglobally Lipschitz
continuous coefficients.
Ann. Appl. Probab.
22 (2012), no. 4, 16111641.
[arXiv].
 Jentzen, A. and Röckner, M.,
Regularity analysis for stochastic partial differential
equations with nonlinear multiplicative trace class noise.
J.
Differential Equations
252 (2012),
no. 1, 114136.
[arXiv].
 Hutzenthaler, M. and Jentzen, A.,
Convergence of the
stochastic Euler scheme
for locally Lipschitz coefficients.
Found.
Comput. Math.
11 (2011), no. 6, 657706.
[arXiv].

Jentzen, A. and Kloeden, P. E.,
Taylor Approximations for Stochastic
Partial Differential Equations.
CBMSNSF Regional Conference
Series in Applied Mathematics
83,
Society for Industrial and Applied
Mathematics (SIAM), Philadelphia, PA, 2011. xiv+211 pp.
 Jentzen, A., Kloeden, P. E. and Winkel, G.,
Efficient simulation of nonlinear parabolic SPDEs
with additive noise.
Ann. Appl. Probab.
21 (2011), no. 3, 908950.
[arXiv].
 Hutzenthaler, M., Jentzen, A. and Kloeden, P. E.,
Strong and weak divergence in finite time of
Euler's method for stochastic differential
equations with nonglobally Lipschitz continuous
coefficients.
Proc. R. Soc. A
467 (2011), no. 2130, 15631576.
[arXiv].
 Jentzen, A.,
Higher order pathwise numerical approximations
of SPDEs with additive noise.
SIAM J. Numer. Anal.
49 (2011),
no. 2, 642667.
 Jentzen, A.,
Taylor expansions of
solutions of stochastic partial
differential equations.
Discrete Contin.
Dyn. Syst. Ser. B
14 (2010), no. 2, 515557.
[arXiv].
 Jentzen, A. and Kloeden, P. E.,
Taylor expansions of solutions of stochastic
partial differential equations with
additive noise.
Ann. Probab.
38 (2010), no. 2, 532569.
[arXiv].
 Jentzen, A., Leber, F., Schneisgen, D., Berger, A.
and Siegmund., S.,
An improved maximum allowable
transfer interval for Lpstability
of networked control systems.
IEEE Trans. Automat. Control
55 (2010),
no. 1, 179184.
 Jentzen, A. and Kloeden, P. E.,
A unified existence and uniqueness theorem
for stochastic evolution equations.
Bull. Aust. Math. Soc.
81 (2010),
no. 1, 3346.
 Jentzen, A. and Kloeden, P. E.,
The numerical approximation of stochastic partial
differential equations.
Milan
J. Math.
77 (2009), no. 1, 205244.
 Jentzen, A., Kloeden, P. E. and Neuenkirch, A.,
Pathwise convergence of numerical
schemes for random and stochastic differential
equations.
Foundations
of Computational Mathematics, Hong Kong 2008, 140161, London Mathematical Society
Lecture Note Series, 363,
Cambridge University Press, Cambridge, 2009.
 Jentzen, A.,
Pathwise numerical approximations of
SPDEs with additive noise under nonglobal Lipschitz coefficients.
Potential
Anal. 31 (2009), no. 4, 375404.
 Jentzen, A. and Kloeden, P. E.,
Pathwise Taylor schemes
for random ordinary differential
equations.
BIT 49 (2009), no. 1, 113140.
 Jentzen, A., Kloeden, P. E. and Neuenkirch, A.,
Pathwise approximation of stochastic
differential equations on domains: higher order
convergence rates without global Lipschitz
coefficients.
Numer.
Math. 112 (2009), no. 1, 4164.
 Jentzen, A. and Neuenkirch, A.,
A random Euler scheme for
Carathéodory differential equations.
J.
Comput. Appl. Math.
224 (2009), no. 1, 346359.
 Jentzen, A. and Kloeden, P. E.,
Overcoming the order barrier
in the numerical approximation of
stochastic partial differential
equations with additive
spacetime noise.
Proc. R. Soc. A
465 (2009),
no. 2102, 649667.
 Kloeden, P. E. and Jentzen, A.,
Pathwise convergent higher
order numerical schemes for
random ordinary differential equations.
Proc.
R. Soc. A 463 (2007),
no. 2087, 29292944.
Theses
 Jentzen, A., Taylor Expansions for Stochastic Partial
Differential Equations.
PhD thesis (2009), Frankfurt University, Germany.
 Jentzen, A., Numerische Verfahren hoher Ordnung
für zufällige Differentialgleichungen.
Diploma thesis (2007), Frankfurt University, Germany.
