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