On Besov regularity of Brownian motions in infinite dimensions

• Autorzy: Hytönen T. P. , Veraar M. C.
• Języki publikacji: EN

Abstrakty

EN

We extend to the vector-valued situation some earlier work of Ciesielski and Roynette on the Besov regularity of the paths of the classical Brownian motion.We also consider a Brownian motion as a Besov space valued random variable. It turns out that a Brownian motion, in this interpretation, is a Gaussian random variable with some pathological properties. We prove estimates for the first moment of the Besov norm of a Brownian motion. To obtain such results we estimate expressions of the form E sup_n­1‖ξn‖, where ξn are independent centered Gaussian random variables with values in a Banach space. Using isoperimetric inequalities we obtain two-sided inequalities in terms of the first moments and the weak variances of ξn.

Słowa kluczowe

EN

Gaussian random variable; maximal estimates; Besov–Orlicz norm; non-separable Banach space; sample path

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2008
• Tom: Vol. 28, Fasc. 1
• Strony: 143--162
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Hytönen T. P.

• Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2B, FI-00014 Helsinki, Finland

autor

Veraar M. C.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warsaw, Poland

Bibliografia

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