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Fakultät für Mathematik
Anschrift
Thea-Leymann-Str. 9
45127 Essen
45127 Essen
Raum
WSC-W-3.21
Telefon
Telefax
Funktionen
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Professor/in, Mathematik / Campus Essen
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Dekan, Dekanat Fakultät für Mathematik
Aktuelle Veranstaltungen
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2024 WS
Vergangene Veranstaltungen (max. 10)
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2024 SS
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2023 WS
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2023 SS
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2022 WS
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.
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Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential EquationsIn: Memoirs of the American Mathematical Society Jg. 296 (2024) Nr. 1481, S. 1 - 90Online Volltext: dx.doi.org/ (Open Access)
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On the Itô-Alekseev-Gröbner formula for stochastic differential equationsIn: Annales de l'Institut Henri Poincaré (B): Probability and Statistics Jg. 60 (2024) Nr. 2, S. 904 - 922Online Volltext: dx.doi.org/ (Open Access)
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An overview on deep learning-based approximation methods for partial differential equationsIn: Discrete and Continuous Dynamical Systems: Series B (DCDS-B) Jg. 28 (2023) Nr. 6, S. 3697 - 3746Online Volltext: dx.doi.org/ (Open Access)
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Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equationsIn: Journal of Numerical Mathematics Jg. 31 (2023) Nr. 1, S. 1 - 28Online Volltext: dx.doi.org/ (Open Access)
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Costly defense traits in structured populationsIn: ALEA: Latin American Journal of Probability and Mathematical Statistics Jg. 19 (2022) Nr. 2, S. 1697 - 1752Online Volltext: dx.doi.org/ (Open Access)
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Multilevel Picard approximations for McKean-Vlasov stochastic differential equationsIn: Journal of Mathematical Analysis and Applications Jg. 507 (2022) Nr. 1, 125761Online Volltext: dx.doi.org/ (Open Access)
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Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functionsIn: Applied Numerical Mathematics Jg. 181 (2022) S. 151 - 175Online Volltext: dx.doi.org/ (Open Access)
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On the speed of convergence of Picard iterations of backward stochastic differential equationsIn: Probability, Uncertainty and Quantitative Risk Jg. 7 (2022) Nr. 2, S. 133 - 150Online Volltext: dx.doi.org/ (Open Access)
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Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent NonlinearitiesIn: Foundations of Computational Mathematics Jg. 22 (2022) Nr. 4, S. 905 - 966Online Volltext: dx.doi.org/ (Open Access)
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Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-normsIn: Journal of Computational and Applied Mathematics Jg. 413 (2022) 114391Online Volltext: dx.doi.org/ (Open Access)
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A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbationsIn: Annales de l'Institut Henri Poincaré (B): Probability and Statistics Jg. 57 (2021) Nr. 2, S. 603 - 626Online Volltext: dx.doi.org/ (Open Access)
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Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensionsIn: IMA Journal of Numerical Analysis Jg. 41 (2021) Nr. 1, S. 493 - 548Online Volltext: dx.doi.org/ Online Volltext (Open Access)
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Differentiability of semigroups of stochastic differential equations with Hölder-continuous diffusion coefficientsIn: ALEA: Latin American Journal of Probability and Mathematical Statistics Jg. 18 (2021) Nr. 1, S. 309 - 324Online Volltext: dx.doi.org/ (Open Access)
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Multilevel Picard iterations for solving smooth semilinear parabolic heat equationsIn: Partial Differential Equations and Applications Jg. 2 (2021) Nr. 6, 80Online Volltext: dx.doi.org/ (Open Access)
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On existence and uniqueness properties for solutions of stochastic fixed point equationsIn: Discrete and Continuous Dynamical Systems: Series B (DCDS-B) Jg. 26 (2021) Nr. 9, S. 4927 - 4962Online Volltext: dx.doi.org/ (Open Access)
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On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equationsIn: Stochastics and Dynamics (SD) Jg. 21 (2021) Nr. 08, 2150048Online Volltext: dx.doi.org/ (Open Access)
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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equationsIn: Partial Differential Equations and Applications Jg. 1 (2020) Nr. 2, 10Online Volltext: dx.doi.org/ (Open Access)
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Multilevel picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearitiesIn: SIAM Journal on Numerical Analysis Jg. 58 (2020) Nr. 2, S. 929 - 961Online Volltext: dx.doi.org/ (Open Access)
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Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential EquationsIn: Communications in Computational Physics (CiCP) Jg. 28 (2020) Nr. 5, S. 2109 - 2138Online Volltext: dx.doi.org/ (Open Access)
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On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficientsIn: The Annals of Probability Jg. 48 (2020) Nr. 1, S. 53 - 93Online Volltext: dx.doi.org/ (Open Access)
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Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risksIn: Electronic Journal of Probability Jg. 25 (2020) S. 101Online Volltext: dx.doi.org/ (Open Access)
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Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximationsIn: Journal of Numerical Mathematics Jg. 28 (2020) Nr. 4, S. 197 - 222Online Volltext: dx.doi.org/ (Open Access)
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Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations : Overcoming the curse of dimensionalityIn: Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences Jg. 476 (2020) Nr. 2244, S. 20200072Online Volltext: dx.doi.org/ (Open Access)
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Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regimeIn: The Annals of Applied Probability Jg. 30 (2020) Nr. 5, S. 2311 - 2354Online Volltext: dx.doi.org/ Online Volltext (Open Access)
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On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential EquationsIn: Journal of Scientific Computing Jg. 79 (2019) Nr. 3, S. 1534 - 1571Online Volltext: dx.doi.org/ (Open Access)
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Zufällige Strukturen in der Evolutionsbiologie : Ohne Zufall keine EvolutionIn: Unikate: Berichte aus Forschung und Lehre (2019) Nr. 53: Mathematik - Herausforderung des Nichtlinearen, S. 79 - 88Online Volltext: dx.doi.org/ Online Volltext (Open Access)
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Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equationsIn: Mathematics of Computation (MCOM) Jg. 87 (2018) Nr. 311, S. 1353 - 1413Online Volltext: dx.doi.org/ (Open Access)
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Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equationsIn: Communications in Mathematical Sciences Jg. 16 (2018) Nr. 6, S. 1489 - 1529Online Volltext: dx.doi.org/ (Open Access)
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Loss of regularity for Kolmogorov equationsIn: The Annals of Probability Jg. 43 (2015) Nr. 2, S. 468 - 527Online Volltext: dx.doi.org/ (Open Access)
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Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficientsIn: Memoirs of the American Mathematical Society Jg. 236 (2015) Nr. 1112,Online Volltext: dx.doi.org/
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Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equationsIn: The Annals of Applied Probability Jg. 23 (2013) Nr. 5, S. 1913 - 1966Online Volltext: dx.doi.org/
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Ecological and genetic effects of introduced species on their native competitorsIn: Theoretical Population Biology Jg. 84 (2013) S. 25 - 35Online Volltext: dx.doi.org/
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Interacting diffusions and trees of excursions : convergence and comparisonIn: Electronic journal of probability : EJP Jg. 17 (2012) Nr. paper no. 71,Online Volltext: dx.doi.org/
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Norovirus GII.4 and GII.7 capsid sequences undergo positive selection in chronically infected patientsIn: Infection, genetics and evolution Jg. 12 (2012) Nr. 2, S. 461 - 466Online Volltext: dx.doi.org/
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Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficientsIn: The annals of applied probability Jg. 22 (2012) Nr. 4, S. 1611 - 1641Online Volltext: dx.doi.org/
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Convergence of the Stochastic Euler Scheme for Locally Lipschitz CoefficientsIn: Foundations of computational mathematics Jg. 11 (2011) Nr. 6, S. 657 - 706Online Volltext: dx.doi.org/
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Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficientsIn: Proceedings of the Royal Society of London. Series A Jg. 467 (2011) Nr. 2130, S. 1563 - 1576Online Volltext: dx.doi.org/
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Supercritical branching diffusions in random environmentIn: Electronic communications in probability : ECP Jg. 16 (2011) Nr. paper no. 69, S. 781 - 791
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Time reversal of some stationary jump diffusion processes from population geneticsIn: Advances in Applied Probability Jg. 42 (2010) Nr. 4, S. 1147 - 1171
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Survival, Extinction and Ergodicity in a Spatially Continuous Population ModelIn: Markov Processes and Related Fields Jg. 15 (2009) Nr. 3, S. 265 - 288
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The Virgin Island ModelIn: Electronic journal of probability : EJP Jg. 14 (2009) Nr. paper no. 39, S. 1117 - 1161
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Ergodic Behavior of Locally Regulated Branching PopulationsIn: The annals of applied probability Jg. 17 (2007) Nr. 2, S. 474 - 501Online Volltext: dx.doi.org/
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Graphical representation of some duality relations in stochastic population modelsIn: Electronic communications in probability : ECP Jg. 12 (2007) Nr. paper no. 21, S. 206 - 220
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Stochastic averaging for multiscale Markov processes with an application to branching random walk in random environment(2015)
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Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations(2014)
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On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients(2014)
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Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries(2014)