On Besov regularity of Brownian motions

Prelegent(ci)

Mark Veraar

Afiliacja

IM PAN

Termin

22 marca 2007 12:15

Pokój

p. 5850

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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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 $\E \sup_{n\geq 1}\|\xi_n\|$, where the $\xi_n$ 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 $\xi_n$.

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