On Besov regularity of Brownian motions in infinite dimensions
| dc.creator | Hytonen, Tuomas | |
| dc.creator | Veraar, Mark | |
| dc.date | 2008-01-18 | |
| dc.date.accessioned | 2026-07-07T08:55:24Z | |
| dc.date.available | 2026-07-07T08:55:24Z | |
| dc.description | 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 $\E \sup_{n\geq 1}\|ξ_n\|$, where the $ξ_n$ 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 $ξ_n$. | |
| dc.description | to appear in Probab. Math. Statist (2008) | |
| dc.identifier | https://arxiv.org/abs/0801.2959 | |
| dc.identifier | http://arxiv.org/abs/0801.2959 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146258 | |
| dc.subject | Probability | |
| dc.subject | Functional Analysis | |
| dc.subject | 60J65; 28C20; 46E40; 60G17 | |
| dc.title | On Besov regularity of Brownian motions in infinite dimensions | |
| dc.type | text |