Some closure properties of multivariate regularly varying distributions

Let X and Y be two independent regularly varying vectors of finite dissension. Take any deterministic bilinear map F and consider Z = F(X,Y). We will present sufficient conditions under which Z is also a regularly varying vector. If time permits, we will apply this results the multidimensional random difference equation and obtain new limit results in the presence of multiplicative noise with regularly varying distribution. The talk is based on a joint work with Thomas Mikosch.