Projects per year
Organization profile
Organisation profile
This research unit has two permanent members: U. Einmahl (Probability and Mathematical Statistics) and T.Kadankova (Stochastic processes and their applications). The other two members, J. Dony (postdoc) and A. Van Messem (Ph. D. Student), do research in mathematical and applied statistics. The research by Uwe Einmahl focuses on limit theorems of probability in general spaces. Classical probability theory deals mainly with random variables taking values in the real line is well developed, but there are many open questions for random variables taking values in infinitedimensional spaces. For instance, there is no natural extension of the classical central limit theorem to Banach spaces. Also the socalled law of the iterated logarithm which in the classical setting was established in 1942 has only relatively recently (1986) been obtained for infinitedimensional spaces. The most recent research by U. Einmahl has addressed not only theoretical questions such as refinements of the basic limit theorems, but also applications to statistics such as density estimation which are possible via socalled empirical processes since these processes can be considered as random elements in a suitable infinitedimensional space. Tetyana Kadankova's research is concerned with Lévy processes, especially with socalled one and twosided exit problems for such processes. A problem which she has recently investigated is determining the laws of the first passage of a level (the first exit time from a fixed interval) by such processes. Lévy processes are considered interesting objects both for the theory and applications. For this reason, this class of stochastic processes has received much attention during the last years. Some important applications of this topic come from financial mathematics and insurance. Oscillating Lévy processes serve also as governing processes for oscillating queueing systems and thus they are also important in queueing theory. Another part of her research is devoted to semiMarkov random walks and compound renewal processes. Additionally, she studies stochastic processes reflected at their infimum (supremum) which serve as governing processes in various applications. Julia Dony has an FWO postdoc position (20082011) and she works on applications of empirical process theory to nonparametric statistics. This is the continuation of her Ph.D. Thesis (under the guidance of U. Einmahl and D. Mason, copromotor) which she defended in May 2008 at the VUB. Arnout van Messem currently works on a Ph. D. Thesis (under the guidance of U. Einmahl and A. Christmann, copromotor) which he will defend during the academic year 2010/11. The main topic of this thesis are socalled support vector machines which are important objects in " robust" statistics.
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Projects
 4 Finished


FWOKN98: General limitestablishment in the chancetheory and empiric process.
1/01/01 → 31/12/01
Project: Fundamental

FWOKN25: General limit theorems in probobility and local Empirical Processes.
1/01/97 → 31/12/98
Project: Fundamental

Research output

Cluster sets for partial sums and partial sum processes
Einmahl, U. & Kuelbs, J., 2014, In : Annals of Probability. 42, p. 11211160 40 p.Research output: Contribution to journal › Article

Consistency and Robustness Properties of Support Vector Machines for HeavyTailed Distributions
Van Messem, A., 28 May 2011, VUB PhD Day, May 28, 2010, Brussels (Belgium). (VUB PhD Day, May 28, 2010, Brussels (Belgium)).Research output: Chapter in Book/Report/Conference proceeding › Meeting abstract (Book) › Research

A Review on Consistency and Robustness Properties of Support Vector Machines for HeavyTailed Distributions
Van Messem, A., Christmann, A., Bock, H. (ed.), Gaul, W. (ed.), Okada, A. (ed.) & Vichi, M. (ed.), Sep 2010, In : Advances in Data Analysis and Classification. 23, 4, p. 199220 22 p.Research output: Contribution to journal › Article

"Busy period, virtual waiting time and number of customers in $ G^{\delta} M^{\varkappa}1B$ system"
Kadankova, T. & Kadankov, V., 2010, In : Queueing Systems. 65(2), p. 175209 35 p.Research output: Contribution to journal › Article

Fast and Robust estimation of the Multivariate Errors in Variables Model
Croux, C., Fekri, M. & RuizGazen, A., 2010, In : Test. 19, 2, p. 286303 18 p.Research output: Contribution to journal › Article
Activities

Mathematical Statistics and Limit Theorems
Uwe Einmahl (Keynote speaker)20 Jun 2013 → 21 Jun 2013Activity: Talk or presentation › Talk or presentation at a workshop/seminar

Probability and Analysis (Conference in honor of Professor Kwapien)
Uwe Einmahl (Keynote speaker)10 Jun 2012 → 16 Jun 2012Activity: Talk or presentation › Talk or presentation at a conference

BSL 2012
Uwe Einmahl (Invited speaker)5 Jun 2012 → 7 Jun 2012Activity: Talk or presentation › Talk or presentation at a conference

10th German Probability and Statistics Days
Uwe Einmahl (Speaker)6 Mar 2012 → 9 Mar 2012Activity: Talk or presentation › Talk or presentation at a conference

International Symposium on Recent Advances in Statistics and Probability in honor of Prof. dr. Noël Veraverbeke
Tetyana Kadankova (Keynote speaker)19 May 2011 → 20 May 2011Activity: Talk or presentation › Talk or presentation at a conference