Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Mark Podolskij
Universität Heidelberg
Inference for Brownian semistationary processes
We introduce a new class of continuous stochastic processes called Brownian semistationary processes
(BSS). We derive limit theorems for functionals of high frequency observations of BSS processes and
apply them for the estimation of the scaling parameter of the unobserved path. Furthermore, we present
the link to turbulence modelling. This talk is based on the joint work with Ole Barndorff-Nielsen and Jose
Manuel Corcuera.
Literatur
O. E. Barndorff-Nielsen, J. M. Corcuera and M. Podolskij (2010). Multipower variation for Brownian semistationary
processes. To appear in Bernoulli.
O. E. Barndorff-Nielsen, J. M. Corcuera and M. Podolskij (2010). Limit theorems for functionals of higher
order differences of Brownian semi-stationary processes. Working paper.
Paul Ressel
Katholische Universität Eichstätt-Ingolstadt
Multivariate distribution functions, classical mean values, and Archimedean copulas
Functions operating on multivariate distribution and survival functions are characterized, based on a
theorem of Morillas, for which a new proof is presented. These results are applied to determine those
classical mean values on [0,1] n which are distribution functions of probability measures on [0,1] n . As
it turns out, the arithmetic mean plays a universal rôle for the characterization of distribution as well as
survival functions. Another consequence is a far reaching generalisation of Kimberling’s theorem, tightly
connected to Archimedean copulas.
Michael Stolz
Westfälische Wilhelms-Universität Münster/ Ruhr-Universität Bochum
Stein’s method and multivariate normal approximation for random matrices
Let Mn be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed
according to Haar measure. By a classical result of Diaconis and Shahshahani, for large matrix size n, the
vector (Tr(Mn),Tr(M 2 n),...,Tr(M d n )) tends to a vector of independent, (real or complex) Gaussian random
variables. Recently, Jason Fulman has demonstrated that for a single power j (which may grow with n),
a speed of convergence result may be obtained via Stein’s method of exchangeable pairs. In this talk, I
will discuss a multivariate version of Fulman’s result, which is based on joint work with Christian Döbler
(Bochum).
Literatur
Döbler, C. / Stolz, M. (2010), Stein’s method and the multivariate CLT for traces of powers on the compact
classical groups, arXiv:1012.3730
Fulman, J. (2010), Stein’s method, heat kernel, and traces of powers of elements of compact Lie groups,
arXiv:1005.1306
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