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⊂ℝ+ under a symmetric Lévy process X in ℝd 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 ℝd. 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.
@article{1158673332,
author = {Manstavi\v cius, Martynas},
title = {A note about Khoshnevisan--Xiao conjecture},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 1635-1640},
language = {en},
url = {http://dml.mathdoc.fr/item/1158673332}
}
Manstavičius, Martynas. A note about Khoshnevisan–Xiao conjecture. Ann. Probab., Tome 34 (2006) no. 1, pp. 1635-1640. http://gdmltest.u-ga.fr/item/1158673332/