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Prof. Dr. Martin Hutzenthaler

Fakultät für Mathematik

Anschrift
Thea-Leymann-Str. 9
45127 Essen
Raum
WSC-W-3.21
Telefon
+49 201 183 68 44
Telefax
+49 201 183 24 26
E-Mail
martin.hutzenthaler@uni-due.de;dekan.mathematik@uni-due.de

Funktionen

  • Professor/in, Mathematik / Campus Essen

  • Dekan, Dekanat Fakultät für Mathematik

Die folgenden Publikationen sind in der Online-Universitätsbibliographie der Universität Duisburg-Essen verzeichnet. Weitere Informationen finden Sie gegebenenfalls auch auf den persönlichen Webseiten der Person.

    Artikel in Zeitschriften

  • Jordan, Felix; Hutzenthaler, Martin; Metzler, Dirk
    Selection for altruistic defense in structured populations
    In: Theoretical Population Biology, Jg. 161, 2025, S. 13 – 24
    DOI (Open Access)
  • Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf
    Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations
    In: Memoirs of the American Mathematical Society, Jg. 296, 2024, Nr. 1481, S. 1 – 90
    DOI, Online Volltext (Open Access)
  • Hudde, Anselm; Hutzenthaler, Martin; Jentzen, Arnulf; Mazzonetto, Sara
    On the Itô-Alekseev-Gröbner formula for stochastic differential equations
    In: Annales de l'Institut Henri Poincaré (B): Probability and Statistics, Jg. 60, 2024, Nr. 2, S. 904 – 922
    DOI, Online Volltext (Open Access)
  • Beck, Christian; Hutzenthaler, Martin; Jentzen, Arnulf; Kuckuck, Benno
    An overview on deep learning-based approximation methods for partial differential equations
    In: Discrete and Continuous Dynamical Systems: Series B (DCDS-B), Jg. 28, 2023, Nr. 6, S. 3697 – 3746
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Anh Nguyen, Tuan
    Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
    In: Journal of Numerical Mathematics, Jg. 31, 2023, Nr. 1, S. 1 – 28
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jordan, Felix; Metzler, Dirk
    Costly defense traits in structured populations
    In: ALEA: Latin American Journal of Probability and Mathematical Statistics, Jg. 19, 2022, Nr. 2, S. 1697 – 1752
    DOI (Open Access)
  • Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
    Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
    In: Journal of Mathematical Analysis and Applications, Jg. 507, 2022, Nr. 1, 125761
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Nguyen, Tuan Anh
    Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions
    In: Applied Numerical Mathematics, Jg. 181, 2022, S. 151 – 175
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
    On the speed of convergence of Picard iterations of backward stochastic differential equations
    In: Probability, Uncertainty and Quantitative Risk, Jg. 7, 2022, Nr. 2, S. 133 – 150
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
    Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent Nonlinearities
    In: Foundations of Computational Mathematics, Jg. 22, 2022, Nr. 4, S. 905 – 966
    DOI (Open Access)
  • Hutzenthaler, Martin; Nguyen, Tuan Anh
    Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms
    In: Journal of Computational and Applied Mathematics, Jg. 413, 2022, 114391
    DOI, Online Volltext (Open Access)
  • Hudde, Anselm; Hutzenthaler, Martin; Mazzonetto, Sara
    A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations
    In: Annales de l'Institut Henri Poincaré (B): Probability and Statistics, Jg. 57, 2021, Nr. 2, S. 603 – 626
    DOI, Online Volltext (Open Access)
  • Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf; van Neerven, Jan; Welti, Timo
    Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions
    In: IMA Journal of Numerical Analysis, Jg. 41, 2021, Nr. 1, S. 493 – 548
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Pieper, Daniel
    Differentiability of semigroups of stochastic differential equations with Hölder-continuous diffusion coefficients
    In: ALEA: Latin American Journal of Probability and Mathematical Statistics, Jg. 18, 2021, Nr. 1, S. 309 – 324
    DOI (Open Access)
  • Weinan, E.; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; E, Weinan
    Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
    In: Partial Differential Equations and Applications, Jg. 2, 2021, Nr. 6, 80
    DOI (Open Access)
  • Beck, Christian; Gonon, Lukas; Hutzenthaler, Martin; Jentzen, Arnulf
    On existence and uniqueness properties for solutions of stochastic fixed point equations
    In: Discrete and Continuous Dynamical Systems: Series B (DCDS-B), Jg. 26, 2021, Nr. 9, S. 4927 – 4962
    DOI, Online Volltext (Open Access)
  • Beck, Christian; Hutzenthaler, Martin; Jentzen, Arnulf
    On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations
    In: Stochastics and Dynamics (SD), Jg. 21, 2021, Nr. 08, 2150048
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
    A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
    In: Partial Differential Equations and Applications, Jg. 1, 2020, Nr. 2, 10
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Kruse, Thomas
    Multilevel picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities
    In: SIAM Journal on Numerical Analysis, Jg. 58, 2020, Nr. 2, S. 929 – 961
    DOI, Online Volltext (Open Access)
  • Becker, Sebastian; Braunwarth, Ramon; Hutzenthaler, Martin; Jentzen, Arnulf; von Wurstemberger, Philippe
    Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations
    In: Communications in Computational Physics (CiCP), Jg. 28, 2020, Nr. 5, S. 2109 – 2138
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf
    On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
    In: The Annals of Probability, Jg. 48, 2020, Nr. 1, S. 53 – 93
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf; Wurstemberger, Philippe von
    Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
    In: Electronic Journal of Probability, Jg. 25, 2020, S. 101
    DOI (Open Access)
  • Beck, Christian; Hornung, Fabian; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
    Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations
    In: Journal of Numerical Mathematics, Jg. 28, 2020, Nr. 4, S. 197 – 222
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Anh Nguyen, Tuan; von Wurstemberger, Philippe
    Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations : Overcoming the curse of dimensionality
    In: Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Jg. 476, 2020, Nr. 2244, S. 20200072
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Pieper, Daniel
    Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regime
    In: The Annals of Applied Probability, Jg. 30, 2020, Nr. 5, S. 2311 – 2354
    DOI, Online Volltext (Open Access)
  • Weinan, E.; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
    On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations
    In: Journal of Scientific Computing, Jg. 79, 2019, Nr. 3, S. 1534 – 1571
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Winter, Anita
    Zufällige Strukturen in der Evolutionsbiologie : Ohne Zufall keine Evolution
    In: Unikate: Berichte aus Forschung und Lehre, 2019, Nr. 53: Mathematik - Herausforderung des Nichtlinearen, S. 79 – 88
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf; Wang, Xiaojie
    Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations
    In: Mathematics of Computation (MCOM), Jg. 87, 2018, Nr. 311, S. 1353 – 1413
    DOI, Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf; Salimova, Diyora
    Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations
    In: Communications in Mathematical Sciences, Jg. 16, 2018, Nr. 6, S. 1489 – 1529
    DOI, Online Volltext (Open Access)
  • Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf
    Loss of regularity for Kolmogorov equations
    In: The Annals of Probability, Jg. 43, 2015, Nr. 2, S. 468 – 527
    DOI (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf
    Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
    In: Memoirs of the American Mathematical Society, Jg. 236, 2015, Nr. 1112
    DOI
  • Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
    Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
    In: The Annals of Applied Probability, Jg. 23, 2013, Nr. 5, S. 1913 – 1966
    DOI
  • Wittmann, Meike J.; Metzler, Dirk; Hutzenthaler, Martin; Gabriel, Wilfried
    Ecological and genetic effects of introduced species on their native competitors
    In: Theoretical Population Biology, Jg. 84, 2013, S. 25 – 35
    DOI
  • Hutzenthaler, Martin
    Interacting diffusions and trees of excursions : convergence and comparison
    In: Electronic Journal of Probability, Jg. 17, 2012, Nr. paper no. 71
    DOI
  • Hoffmann, Dieter; Protzer, Ulrike; Menzel, Helge; Umgelter, Andreas; Panning, Marcus; Seebach, Judith; Hutzenthaler, Martin
    Norovirus GII.4 and GII.7 capsid sequences undergo positive selection in chronically infected patients
    In: Infection, Genetics and Evolution, Jg. 12, 2012, Nr. 2, S. 461 – 466
    DOI
  • Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
    Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
    In: The Annals of Applied Probability, Jg. 22, 2012, Nr. 4, S. 1611 – 1641
    DOI
  • Hutzenthaler, Martin; Jentzen, Arnulf
    Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients
    In: Foundations of Computational Mathematics, Jg. 11, 2011, Nr. 6, S. 657 – 706
    DOI
  • Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
    Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
    In: Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Jg. 467, 2011, Nr. 2130, S. 1563 – 1576
    DOI
  • Hutzenthaler, Martin
    Supercritical branching diffusions in random environment
    In: Electronic Communications in Probability, Jg. 16, 2011, Nr. paper no. 69, S. 781 – 791
    Online Volltext
  • Hutzenthaler, Martin; Taylor, Jesse Earl
    Time reversal of some stationary jump diffusion processes from population genetics
    In: Advances in Applied Probability, Jg. 42, 2010, Nr. 4, S. 1147 – 1171
    Online Volltext
  • Hutzenthaler, Martin; Etheridge, A.M.; Berestycki, Julien
    Survival, Extinction and Ergodicity in a Spatially Continuous Population Model
    In: Markov Processes and Related Fields, Jg. 15, 2009, Nr. 3, S. 265 – 288
    Online Volltext
  • Hutzenthaler, Martin
    The Virgin Island Model
    In: Electronic journal of probability : EJP, Jg. 14, 2009, Nr. paper no. 39, S. 1117 – 1161
    Online Volltext
  • Hutzenthaler, Martin; Wakolbinger, Anton
    Ergodic Behavior of Locally Regulated Branching Populations
    In: The annals of applied probability, Jg. 17, 2007, Nr. 2, S. 474 – 501
    DOI
  • Hutzenthaler, Martin; Alkemper, Roland
    Graphical representation of some duality relations in stochastic population models
    In: Electronic communications in probability : ECP, Jg. 12, 2007, Nr. paper no. 21, S. 206 – 220
    Online Volltext

    • Preprints

  • Hutzenthaler, Martin; Jordan, Felix; Metzler, Dirk
    Altruistic defense traits in structured populations
    2015
    Online Volltext (Open Access)
  • Hutzenthaler, Martin; Pfaffelhuber, Peter
    Stochastic averaging for multiscale Markov processes with an application to branching random walk in random environment
    2015
    Online Volltext (Open Access)
  • Hutzenthaler, Martin; Jentzen, Arnulf; Noll, Marco
    Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries
    2014
    Online Volltext (Open Access)