*Tid:***28 augusti 2006 kl 15.15-16.00 **

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

*Föredragshållare:***Filip Lindskog
**

* Titel: *
Regular variation and the Cramér-Wold device. (Docentföreläsning)

* Sammanfattning: *
Regular variation appears in a natural way in many areas of
applied probability such as extreme value theory, queuing
theory, point process theory, renewal theory, and summation
theory for random variables and vectors. In particular, regular
variation appears in necessary and sufficient conditions for
convergence in distribution of normalized partial sums and
component-wise maxima of independent and identically distributed
random vectors. Moreover, many types of non-linear time series
have regularly varying stationary distributions, and empirical
studies of financial and insurance loss data support the
assumption of regular variation in statistical methods for risk
management. Similar to weak convergence of probability measures
(convergence in distribution), regular variation is a
particularly simple concept in the univariate case. A natural
question, with the Cramér-Wold device in mind, is therefore
whether regular variation for linear combinations of the
components of a random vector implies regular variation for the
vector. This question has particular relevance for the study of
stationary solutions to time series which can be formulated in
terms of random difference equations.

This presentation is based on parts of joint work with Henrik Hult and with Jan Boman.