Capacities in Wiener Space, Quasi-Sure Lower Functions, and Kolmogorov's Epsilon-Entropy
| dc.creator | Khoshnevisan, Davar | |
| dc.creator | Levin, David A. | |
| dc.creator | Mendez-Hernandez, Pedro J. | |
| dc.date | 2004-10-09 | |
| dc.date.accessioned | 2026-07-07T05:13:06Z | |
| dc.date.available | 2026-07-07T05:13:06Z | |
| dc.description | We propose a set-indexed family of capacities $\{\cap_G \}_{G \subseteq \R_+}$ on the classical Wiener space $C(\R_+)$. This family interpolates between the Wiener measure ($\cap_{\{0\}}$) on $C(\R_+)$ and the standard capacity ($\cap_{\R_+}$) on Wiener space. We then apply our capacities to characterize all quasi-sure lower functions in $C(\R_+)$. In order to do this we derive the following capacity estimate which may be of independent interest: There exists a constant $a > 1$ such that for all $r > 0$, \[ \frac {1}{a} \K_G(r^6) e^{-π^2/(8r^2)} \le \cap_G \{f^* \le r\} \le a \K_G(r^6) e^{-π^2/(8r^2)}. \] Here, $\K_G$ denotes the Kolmogorov $ε$-entropy of $G$, and $f^* := \sup_{[0,1]}|f|$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0410236 | |
| dc.identifier | http://arxiv.org/abs/math/0410236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72822 | |
| dc.subject | Probability | |
| dc.subject | 60J45 (Primary) 60J65, 28C20 (Secondary) | |
| dc.title | Capacities in Wiener Space, Quasi-Sure Lower Functions, and Kolmogorov's Epsilon-Entropy | |
| dc.type | text |