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.