On Besov regularity of Brownian motions
- Speaker(s)
- Mark Veraar
- Affiliation
- IM PAN
- Date
- March 22, 2007, 12:15 p.m.
- Room
- room 5850
- Seminar
- Seminar of Probability Group
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 $\xi_n$.