Vorträge

Wenn nicht explizit anders angegeben, finden die Vorträge im SR 2.058 (Geb. 20.30) statt.

Dienstag, 10.02.2015

15.45 Uhr Prof. Dr. Anne Leucht (Technische Universität Braunschweig):

Characteristic function based hypothesis tests for time series

Abstract: We establish two consistent L2-type tests for time series data. Besides a test for symmetry, a test for the parametric class of the marginal distribution based on the empirical characteristic function is considered. In particular, the second one is of special interest in financial mathematics since distributions of financial time series often have a complicated density or cumulative distribution function while their characteristic function is simple. Examples include NIG and VG distributions. Our test statistics can be approximated by degenerate V-statistics. Their limit distributions have a complicated form and depend on unknown parameters and the underlying dependence structure in a complicated way. Therefore, (asymptotic) critical values of the tests.

Dienstag, 03.02.2015

15.45 Uhr Prof. Dr. Ralph Neininger (J.W. Goethe-Universität Frankfurt):

Pólya Urns via the contraction method

Abstract: A new approach to analyse the asymptotic behaviour of Pólya urns is discussed which is based on the so-called contraction method. For this, a combinatorial discrete-time embedding of the evolution of the urn process into random rooted trees is developed. A decomposition of these trees leads to a system of recursive distributional equations which capture the distributions of the numbers of balls of each colour. Ideas from the contraction method are used to study such systems of recursive distributional equations asymptotically. We discuss this approach at a couple of concrete Pólya urns that lead to limit laws with normal limit distributions, with non-normal limit distributions and with asymptotic periodic distributional behaviour.

Dienstag, 27.01.2015

15.45 Uhr Dr. Cornelia Wichelhaus (Universität Heidelberg ):

Nichtparametrische Analyse Stochastischer Netzwerke

Abstract: Stochastische Netzwerke sind interagierende Systeme von Knoten mit Bedienstationen, zwischen denen sich Kunden bewegen. Typische Anwendungsfelder dieser Modelle sind Kommunikationsnetze, Produkti-onsanlagen, dynamische Populationsmodelle und Modelle aus den Verkehrswissenschaften. Der Vortrag stellt nichtparametische Schätzprobleme vor, bei denen aufgrund von unvollständigen Beobachtungen der stochastischen Systeme die Bedienzeitverteilungen an den Knoten geschätzt werden müssen. Es werden zwei verschiedene Methoden vorgestellt, die zu stark konsistenten Schätzern führen. Simulationen zeigen die gute Anwendbarkeit der Schätzverfahren. Darüber hinaus wird ein funktionaler Zentraler Grenzwertsatz auf einem diskreten Funktionenraum präsentiert und die Konsistenz einer Bootstraptechnik gezeigt.

Dienstag, 13.01.2015

15.45 Uhr Prof. Dr. Marie Hušková (Karls-Universität Prag):

Tests for Time Series of Counts Based on the Probability Generating Function

Abstract: Two type of testing problems will be considered:
(a) goodness-of-fit type tests for distributional assumptions concerning count time series models.
(b) Sequential tests for detecting structural changes in count time series models.
The proposed test statistics are based on the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic proper-ties of these test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as realdata examples.
The talk is based on the joint works with S. Hudecová and S. Meintanis."

Dienstag, 16.12.2014

Ein Ansatz zur exakten Simulation max-stabiler Prozesse

Abstract: The simulation method for mixed moving maxima processes suggested by Schlather (2002) has the disadvantage of being exact only for bounded storm functions with compact support. Here, we present a new, exact method that does not have these restrictions. We show that the new method is to some extend optimal, and demonstrate by an example that the new, exact method can be faster than the approximation by Schlather (2002) for storm function with non-compact support. While the implementation of the former algorithm has been straightforward, the new method needs some more effort for coding. The method has the potential of simulating Brown-Resnick processes exactly."

Dienstag, 25.11.2014

15.45 Uhr M.Sc. Jan Weis (Institut für Stochastik, KIT):

Integralgeometrie von translationsinvarianten Tensorbewertungen

Abstract: Integralgeometrische Formeln sind schon seit Langem für reellwertige Bewertungen auf den konvexen Kör-pern von Interesse. Im tensorwertigen Fall haben Hug, Schneider und Schuster 2008 eine erste Darstellung speziell für Crofton-Integrale gefunden. In diesem Vortrag werden wir solche Crofton-Formeln für translati-onsinvariante intrinsische Tensorbewertungen herleiten und vereinfachen. Daraus können wir dann auf ein-fache Weise weitere Spezialfälle folgern, die teilweise auf anderem Weg von anderen Autoren schon gezeigt worden sind.

Dienstag, 18.11.2014

15.45 Uhr Prof. Dr. Steffen Dereich (Universität Münster):

Condensation in preferential attachment models with fitness

Abstract: A popular model for complex networks is the preferential attachment model which gained popularity in the end of the 90’s since it gives a simple explanation for the appearance of power laws in real world networks. Mathematically, one considers a sequence of random graphs that is built dynamically according to a simple rule. In each step a new vertex is added and linked randomly by a random or deterministic number of edges to the vertices already present in the system. In this process, links to vertices with high degree are preferred. A variant of the model, additionally, assigns each vertex a random positive fitness (say a -distributed value) which has a linear impact on its attractivity in the network formation. Such network models show a phase transition for compactly supported . In the condensation phase, in the limit, there is a comparably small set of vertices (the condensate) that attracts a constant fraction of new links established by new vertices. This condensation effect was observed for the first time by Bianconi and Bara´ asi in 2001, where it was coined Bose-Einstein phase due to similarities to Bose-Einstein condensation. The fitness of the vertices in the condensate gradually converges to the essential supremum of  and in the talk we discuss the dynamics of this process.