M
Martin Hutzenthaler
Researcher at University of Duisburg-Essen
Publications - 104
Citations - 3162
Martin Hutzenthaler is an academic researcher from University of Duisburg-Essen. The author has contributed to research in topics: Stochastic differential equation & Partial differential equation. The author has an hindex of 26, co-authored 96 publications receiving 2637 citations. Previous affiliations of Martin Hutzenthaler include Goethe University Frankfurt & Ludwig Maximilian University of Munich.
Papers
More filters
Journal ArticleDOI
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
TL;DR: In this article, an explicit and easily implementable numerical method for such an SDE was proposed, which converges strongly with the standard order one-half to the exact solution of the SDE.
Journal ArticleDOI
Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
TL;DR: In this article, it was shown that for a large class of SDEs with non-globally Lipschitz continuous drift and diffusion coefficients, Euler's approximation converges neither in the strong mean-square sense nor in the numerically weak sense to the exact solution at a finite time point.
Book
Numerical Approximations of Stochastic Differential Equations With Non-globally Lipschitz Continuous Coefficients
TL;DR: In this article, moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method were established.
Journal ArticleDOI
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
TL;DR: In this article, a general theory based on rare events was developed for studying integrability properties such as moment bounds for discrete-time stochastic processes, and moment bounds were established for fully and partially driftimplicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method.
Journal ArticleDOI
Loss of regularity for Kolmogorov equations
TL;DR: In this paper, the authors consider the intermediate regime of non-hypoelliptic second-order Kolmogorov PDEs with smooth coefficients and show that the standard Euler approximations may converge to the exact solution of the SDE in strong and numerically weak sense, but at a rate that is slower then any power law.