Abstract

Superpositions of Ornstein-Uhlenbeck type (supOU) processes provide a rich class of stationary stochastic processes for which the marginal distribution and the dependence structure may be modeled independently [1,2]. We investigate the limiting behavior of integrated supOU processes with finite variance[3,4,6] (see also [7] for multifaced behaviour of supOU processes in the case the infinite variance). We show that after suitable normalization four different limiting processes may arise. The type of limit depends on the decay of the correlation function as well as on the characteristic triplet of the marginal distribution. supOU processes, moreover, may exhibit intermittency, a phenomenon affecting the rate of growth of moments[3,4,5,6,8]. The intermittency phenomenon appears also in some other models, for example, in the subclass of ambit processes² known as trawl processes [5]. Joint work with D. Grahovac (Osijek University, Croatia) and M. Taqqu (Boston University, USA ).