*Tid:***5 november 2007 kl 15.15 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Vid seminariet den 5 november diskuteras Jens Svensssons avhandling för tekn.lic.-examen:

**
Some Asymptotic Results in Dependence Modelling
**
Inbjuden diskutant är professor
Allan Gut,
Matematisk statistik,
Uppsala Universitet.

* Sammanfattning: *
This thesis consists of two papers, both devoted to the study of
asymptotics in dependence modelling. The first paper studies large
deviation probabilities for a sum of dependent random variables,
where the dependence stems from a few underlying random variables,
so-called factors. Each summand is composed of two parts: an
idiosyncratic part and a part given by the factors. Conditions
under which both factors and idiosyncratic components contribute
to the large deviation behaviour are found and the resulting
approximation is evaluated in a simple special case. The results
are then applied to stochastic processes with the same structure.
Based on the results of the first part of the paper, it is
concluded that large deviations on a finite time interval are due
to one large jump that can come from either the factor or the
idiosyncratic part of the process.

The second paper studies the asymptotic eigenvalue distribution of the exponentially weighted moving average (EWMA) covariance estimator. Equations for the limiting eigenvalue density and the boundaries of its support are found using the Marcenko-Pastur theorem.