With gaussian processes and between two self-similarities

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
Ore 15:00

Relatore:

• Yuliya Mishura (Taras Shevchenko National University of Kyiv, 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)

Referente: Luca Di Persio