A note about Khoshnevisan--Xiao conjecture
| dc.creator | Manstavičius, Martynas | |
| dc.date | 2006-09-25 | |
| dc.date.accessioned | 2026-07-07T07:25:13Z | |
| dc.date.available | 2026-07-07T07:25:13Z | |
| dc.description | Khoshnevisan and Xiao showed in [Ann. Probab. 33 (2005) 841--878] that the statement about almost surely vanishing Bessel--Riesz capacity of the image of a Borel set $G\subset\mathbb{R}_+$ under a symmetric Lévy process $X$ in $\mathbb{R}^d$ is equivalent to the vanishing of a deterministic $f$-capacity for a particular function $f$ defined in terms of the characteristic exponent of $X$. The authors conjectured that a similar statement is true for all Lévy processes in $\mathbb{R}^d$. We show that the conjecture is true provided we extend the definition of $f$ and require certain integrability conditions which cannot be avoided in general. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117906000000197 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0609696 | |
| dc.identifier | http://arxiv.org/abs/math/0609696 | |
| dc.identifier | Annals of Probability 2006, Vol. 34, No. 4, 1635-1640 | |
| dc.identifier | doi:10.1214/009117906000000197 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116645 | |
| dc.subject | Probability | |
| dc.subject | 60J45 (Primary) 60G51, 60J25 (Secondary) | |
| dc.title | A note about Khoshnevisan--Xiao conjecture | |
| dc.type | text |