- Series
- Stochastics Seminar
- Time
- Thursday, April 4, 2013 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Thomas Mikosch – University of Copenhagen
- Organizer
- Liang Peng
In recent work, an idea of
Adam Jakubowski
was used to prove infinite stable limit theory and
precise large deviation results
for sums of strictly stationary regularly varying sequences.
The idea of Jakubowski consists of approximating tail probabilities
of distributions for such sums with increasing index
by the corresponding quantities
for sums with fixed index. This idea can also be made to work for
Laplace functionals of point processes, the distribution function of
maxima and the characteristic functions of partial sums of stationary
sequences. In each of these situations, extremal
dependence manifests in the appearance of suitable cluster indices
(extremal index for maxima, cluster index for sums,...). The proposed method
can be easily understood and has the potential to function as heuristics for
proving limit results for weakly dependent heavy-tailed sequences.