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<< 2017

Veranstaltungskalender 2018


3 Einträge gefunden

  • Juni
  • 12. Juni
    17:15 - 18:30
    Ort: Geb. 48-210
    Fachbereich Mathematik

    Prof. Dr. Henryk Zähle, Universität des Saarlandes, "On the property of qualitative robustness of statistical point estimators"

    A point estimator is a tool which assigns to each sample (data set) an estimated value of the aspect of interest of the unknown distribution of the data. An estimator is considered qualitatively robust when small changes in the distribution of the data result only in small changes of the distribution of the estimator. After an introduction into statistical models and point estimators I will recall the classical notion of qualitative robustness originated by F. Hampel in the 1970th. Hampel considers qualitative robustness as a global property. This generates a sharp division of estimators into those that are called "robust"' and others that are called "not robust"'. In the last part of the talk I will discuss a recent refinement of Hampel's terminology where qualitative robustness is considered as a local property. I will explain why it can be beneficial to know the sets of relevant distributions on which qualitative robustness holds, and I will present some criteria and examples. This final part is based on joint work with V. Krätschmer (U Duisburg--Essen) and A. Schied (U Waterloo). 
  • Mai
  • 15. Mai
    17:15 - 18:15
    Ort: Raum 48-210
    FB Mathematik

    Prof. Dr. Ingo Steinwart, Universität Stuttgart, "Approximation Properties of RKHS and an Applications to Stochastic Processes"

    Reproducing kernel Hilbert Spaces (RKHS) play an important role in several branches of mathematics including statistical learning theory and stochastic processes. In this talk we will investigate approximation
    properties of RKHS with the help of certain interpolation spaces. Here the main tool is a generalized version of the classical Mercer theorem, which makes it possible to describe these interpolation spaces by
    weighted sequence spaces.
    In the second part we illustrate how the general theory leads to generalized Karhunen-Loeve expansions of stochastic processes. In particular, we discuss their path behavior and our ability to approximate their paths in strong norms.

  • Januar
  • 16. Januar
    17:15 - 18:30
    Ort: Raum 48-210
    Fachbereich Mathematik

    Prof. Dr. Andreas Neuenkirch, Universität Mannheim, "Recent Developments in Numerical Methods for SDEs"

    Stochastic differential equations (SDEs) are an important modeling tool in many areas of science. Since explicit solutions are unknown, one has to rely on numerical methods for the simulation of such SDEs. The traditional convergence analysis for numerical methods relies on the global Lipschitz assumption for the coefficients of the SDEs. However, this is rarely met in practice.

    The last ten years have seen a rapid growth in the numerical analysis of SDEs without the global Lipschitz condition. Examples include superlinear or square root coefficients, which appear e.g. in biology and mathematical finance.
    After an introduction into SDEs and classical numerical results I will give a review of these developments. Moreover, I will present recent findings in the case of discontinuous coefficients. This final part is based on a joint work with M. Szölgyenyi (ETH Zürich) and L. Szpruch (U Edinburgh).