28 września w godzinach 10:15-12:00 w sali WS odbędzie się wykład prof. Thomasa Mikoscha pt. Multivariate regular variation. Streszczenie: The notion of multivariate regular varition (mvr) arises as domain of attraction condition for partial sums of iid random vectors, maxima of iid random variables and in the context of stochastic recurrence equation. In a way, mvr is a natural extension to higher dimensions of power law behavior in the tails of distributions. In the first part of the talk we discuss under which circumstances regular variation of all linear combinations of a random vector implies mvr of the vector. In a second part we discuss under which circumstances the regular variation of a functional of some independent random variables or stochastic processes (such as products of independent variables, stochastic integrals or a linear combination with fixed coefficients) implies regular variation of the underlying independent components. In a third part we discuss extensions of mvr to function spaces and consequences for heavy-tailed large deviation results for partial sum processes of Donsker type.
