----------------------------------------------------------------------------- A v v i s o d i S e m i n a r i o ----------------------------------------------------------------------------- Venerdì 1 Aprile, ore 11 -----------------------------------------------------------------------------

Stanza 34 Dipartimento di Scienze Statistiche "Sapienza" Università di Roma

Prof. Yuliya Mishura (Kyiv University)

*Titolo:* *Between two self-similarities*

*Sintesi:* Everybody knows that fractional Brownian motion with any Hurst index is a self-similar process with stationary increments. According to geometric terminology of J. P. Kahane, it belongs to helix. Self-similarity and incremental stationarity are very useful when we study the properties of different functionals based on fBm however these properties are rather restrictive. For example, Ornstein-Uhlenbeck process starting from zero time point is neither self-similar nor stationary or with stationary increments. Therefore the goal of the present talk is to consider wider class of Gaussian processes. In our terminology, they live between two self-similarities, or belong to the generalized quasi-helix. We consider three problems concerning such processes: --asymptotic behavior of maximal functionals; --representation theorems involving integrals w.r.t. such processes; --some statistical results. The results are common with: Alexander Novikov (Sydney University), Mikhail Zhitlukhin (Steklov Mathematical Institute), Georgij Shevchenko (Kyiv University) and Kostjantin Ralchenko (Kyiv University)

Tutti gli interessati sono invitati a partecipare. Cordiali saluti Alessandro De Gregorio