A convergence theorem for stationary heavy tailed sequences

Seminarium: 
Teoria prawdopodobieństwa i modelowanie stochastyczne
Osoba referująca: 
Azra Tafro (University of Zagreb)
Data: 
czwartek, 30. Marzec 2017 - 12:15
Sala: 
602
Opis: 
Point processes theory is a useful tool for the extremal analysis of stochastic processes. It is well known, for instance, that for an iid sequence of random variables, regular variation of the marginal distribution is equivalent to the convergence of the point process generated by the sequence towards a suitable Poisson point process. That statement then yields many asymptotic distributional properties about the original sequence. There are many extensions of this result to dependent stationary sequences and the point processes generated by them. We will give such a result for a class of weakly dependent regularly varying processes in the multivariate setting. As an application of the result, we will show the invariance principle for the so-called maximal process. This is joint work with Bojan Basrak.