*Seminario congiunto Università Sapienza - Tor Vergata, Roma*

*Mercoledì 3 ottobre 2018*

Ore 15:00, Aula 34 (iv piano)

Dipartimento di Scienze Statistiche, Sapienza

*Titolo: *Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes

*Speaker:* Prof. N. Leonenko (Cardiff University, UK)

*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. In this paper we investigate the limiting behavior of integrated supOU processes with finite 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. We establish this rate for each of the four limiting scenarios. The rate changes at some point indicating that there is a change-point in the asymptotic behavior of absolute moments. For such a behavior to be possible, the moments in the limit theorem do not converge beyond some critical point. We show that this point is related to the dependence structure of the supOU process. The intermittency phenomenon appears also in some other models, for example, Intermittency of trawl processes.

Joint work with D. Grahovac (Osijek University, Croatia) and M. Taqqu (Boston University, USA).

Tutti gli interessati sono invitati ad intervenire.

Cordiali saluti. Luisa Beghin

*************************************************************** Luisa Beghin Dipartimento di Scienze Statistiche Fac. Ingegneria dell'Informazione, Informatica e Statistica "SAPIENZA" Università di Roma Piazzale Aldo Moro 5, 00185 Roma T (+39) 06 49910543 F (+39) 06 4959241 https://sites.google.com/site/luisabeghin/ *****************************************************************