photo Arnulf Jentzen
ETH Zurich

Address:
Arnulf Jentzen
Seminar for Applied Mathematics
Department of Mathematics
ETH Zurich
Rämistrasse 101
8092 Zürich
Switzerland

Office: Room HG G 58.1
Fon (Secretariat): +41 44 633 4766
Fax: +41 44 632 1104
Office hour: on appointment

E-mail: arnulf.jentzen (at) sam.math.ethz.ch
Homepage: http://www.ajentzen.de
Homepage at ETH Zurich: https://www.math.ethz.ch/sam/the-institute/people.html?u=jentzena
Born: November 1983 (age 32)

Links: [Profile on Google Scholar] [Profile on ResearchGate] [Profile on MathSciNet] [ETH Webmail]
Last update of this homepage: July 15th, 2016

Research group

Current members of the research group

  • Sebastian Becker (PhD student at Frankfurt University, Institute of Mathematics, joint supervision with Prof. Dr. Peter E. Kloeden)
  • Prof. Dr. Arnulf Jentzen (Head of the research group)
  • Ryan Kurniawan (PhD Student at ETH Zurich, D-MATH, Seminar for Applied Mathematics)
  • Primoz Pusnik (PhD Student at ETH Zurich, D-MATH, Seminar for Applied Mathematics)
  • Diyora Salimova (Postgraduate student at ETH Zurich, D-MATH, Seminar for Applied Mathematics)
  • Timo Welti (PhD Student at ETH Zurich, D-MATH, Seminar for Applied Mathematics)

Former members of the research group

  • Prof. Dr. Sonja Cox (former Postdoc/Fellow, 2012-2014, now tenure-track Assistant Professor at the University of Amsterdam)
  • Dr. Raphael Kruse (former Postdoc, 2012-2014, now Head of the Junior Reseach Group "Uncertainty Quantification" at the Technical University of Berlin)

Research areas

  • Stochastic analysis (stochastic calculus, well-posedness and regularity analysis for stochastic ordinary and partial differential equations)
  • Numerical analysis (computational stochastics/stochastic numerics, computational finance)
  • Analysis of partial differential equations (well-posedness and regularity analysis for partial differential equations)

Editorial boards affiliations

Preprints and publications that did not yet appear on MathSciNet

  • E, W., Hutzenthaler, M., Jentzen, A., and Kruse, T., On full history recursive multilevel Picard approximations and numerical approximations of high-dimensional nonlinear parabolic partial differential equations. [arXiv] (2016), 27 pages.
  • 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.
  • Hutzenthaler, M., Jentzen, A., and Salimova, D., Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations. [arXiv] (2016), 42 pages.
  • Becker, S. and Jentzen, A., Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations. [arXiv] (2016), 58 pages.
  • Andersson, A., Jentzen, A., and Kurniawan, R., Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values. [arXiv] (2015), 31 pages.
  • 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.
  • Jentzen, A. and Pusnik, P., Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. [arXiv] (2015), 38 pages.
  • Jentzen, A. and Kurniawan, R., Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients. [arXiv] (2015), 51 pages.
  • Conus, D., Jentzen, A. and Kurniawan, R., Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients. [arXiv] (2014), 29 pages.
  • Hutzenthaler, M., Jentzen, A. and Noll, M., Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries. [arXiv] (2014), 32 pages.
  • Hutzenthaler, M. and Jentzen, A., On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients. [arXiv] (2014), 41 pages.
  • 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.
  • Da Prato, G., Jentzen, A. and Röckner, M., A mild Ito formula for SPDEs. [arXiv] (2011), 31 pages.
  • Jentzen, A., Müller-Gronbach, T. and Yaroslavtseva, L., On stochastic differential equations with arbitrary slow convergence rates for strong approximation. [arXiv] (2015), 26 pages. To appear in Communications in Mathematical Sciences.
  • Hutzenthaler, M., Jentzen, A. and Wang, X., Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. [arXiv] (2013), 32 pages. To appear in Mathematics of Computation.
  • Becker, S., Jentzen, A. and Kloeden, P. E., An exponential Wagner-Platen type scheme for SPDEs. [arXiv] (2013), 24 pages. To appear in SIAM Journal on Numerical Analysis.

Publications according to MathSciNet

  • E, W., Jentzen, A. and Shen, H., Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Nonlinear Anal. 142 (2016), no. 142, 152-193. [arXiv].
  • Hutzenthaler, M. and Jentzen, A., Numerical approximations of stochastic differential equations with non-globally 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, 313-362. [arXiv].
  • Hairer, M., Hutzenthaler, M. and Jentzen, A., Loss of regularity for Kolmogorov equations. Ann. Probab. 43 (2015), no. 2, 468-527. [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, 1913-1966. [arXiv].
  • Blömker, D. and Jentzen, A., Galerkin approximations for the stochastic Burgers equation. SIAM J. Numer. Anal. 51 (2013), no. 1, 694-715. [arXiv].
  • Hutzenthaler, M., Jentzen, A. and Kloeden, P. E., Strong convergence of an explicit numerical method for SDEs with non-globally Lipschitz continuous coefficients. Ann. Appl. Probab. 22 (2012), no. 4, 1611-1641. [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, 114-136. [arXiv].
  • Hutzenthaler, M. and Jentzen, A., Convergence of the stochastic Euler scheme for locally Lipschitz coefficients. Found. Comput. Math. 11 (2011), no. 6, 657-706. [arXiv].
  • Jentzen, A. and Kloeden, P. E., Taylor Approximations for Stochastic Partial Differential Equations. CBMS-NSF 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, 908-950. [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 non-globally Lipschitz continuous coefficients. Proc. R. Soc. A 467 (2011), no. 2130, 1563-1576. [arXiv].
  • Jentzen, A., Higher order pathwise numerical approximations of SPDEs with additive noise. SIAM J. Numer. Anal. 49 (2011), no. 2, 642-667.
  • Jentzen, A., Taylor expansions of solutions of stochastic partial differential equations. Discrete Contin. Dyn. Syst. Ser. B 14 (2010), no. 2, 515-557. [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, 532-569. [arXiv].
  • Jentzen, A., Leber, F., Schneisgen, D., Berger, A. and Siegmund., S., An improved maximum allowable transfer interval for Lp-stability of networked control systems. IEEE Trans. Automat. Control 55 (2010), no. 1, 179-184.
  • Jentzen, A. and Kloeden, P. E., A unified existence and uniqueness theorem for stochastic evolution equations. Bull. Aust. Math. Soc. 81 (2010), no. 1, 33-46.
  • Jentzen, A. and Kloeden, P. E., The numerical approximation of stochastic partial differential equations. Milan J. Math. 77 (2009), no. 1, 205-244.
  • 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, 140-161, London Mathematical Society Lecture Note Series, 363, Cambridge University Press, Cambridge, 2009.
  • Jentzen, A., Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients. Potential Anal. 31 (2009), no. 4, 375-404.
  • Jentzen, A. and Kloeden, P. E., Pathwise Taylor schemes for random ordinary differential equations. BIT 49 (2009), no. 1, 113-140.
  • 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, 41-64.
  • Jentzen, A. and Kloeden, P. E., Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. Proc. R. Soc. A 465 (2009), no. 2102, 649-667.
  • Jentzen, A. and Neuenkirch, A., A random Euler scheme for Carathéodory differential equations. J. Comput. Appl. Math. 224 (2009), no. 1, 346-359.
  • 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, 2929-2944.

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.