Prof. Yuliya Mishura  (Kyiv University)

Titolo:

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)