Descrizione: 

Seminario della prof.ssa Yuliya Mishura (Kyiv University, Ukraine).

Abstract
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).

Data: 
01-04-2016
Luogo: 
Dipartimento di Scienze Statistiche; aula 34 (4° p.), p.le A. Moro 5, Roma. Ore 11