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
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 $\xi_n$.