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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

  • 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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ 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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ 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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ 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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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
    Online Volltext: dx.doi.org/ (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,
    Online Volltext: dx.doi.org/
  • 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
    Online Volltext: dx.doi.org/
  • 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
    Online Volltext: dx.doi.org/
  • Hutzenthaler, Martin
    Interacting diffusions and trees of excursions : convergence and comparison
    In: Electronic journal of probability : EJP Jg. 17 (2012) Nr. paper no. 71,
    Online Volltext: dx.doi.org/
  • 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
    Online Volltext: dx.doi.org/
  • 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
    Online Volltext: dx.doi.org/
  • 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
    Online Volltext: dx.doi.org/
  • 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 Jg. 467 (2011) Nr. 2130, S. 1563 - 1576
    Online Volltext: dx.doi.org/
  • Hutzenthaler, Martin
    Supercritical branching diffusions in random environment
    In: Electronic communications in probability : ECP 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
    Online Volltext: dx.doi.org/
  • 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
  • Hutzenthaler, Martin; Pfaffelhuber, Peter
    Stochastic averaging for multiscale Markov processes with an application to branching random walk in random environment
    (2015)
    (Open Access)
  • Cox, Sonja; Hutzenthaler, Martin; Jentzen, Arnulf
    Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations
    (2014)
    Online Volltext
  • Hutzenthaler, Martin; Jentzen, Arnulf
    On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients
    (2014)
    Online Volltext
  • Hutzenthaler, Martin; Jentzen, Arnulf; Noll, Marco
    Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries
    (2014)