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July 2006 A note about Khoshnevisan–Xiao conjecture
Martynas Manstavičius
Ann. Probab. 34(4): 1635-1640 (July 2006). DOI: 10.1214/009117906000000197


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.


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Martynas Manstavičius. "A note about Khoshnevisan–Xiao conjecture." Ann. Probab. 34 (4) 1635 - 1640, July 2006.


Published: July 2006
First available in Project Euclid: 19 September 2006

zbMATH: 1101.60030
MathSciNet: MR2257660
Digital Object Identifier: 10.1214/009117906000000197

Primary: 60J45
Secondary: 60G51 , 60J25

Keywords: Bessel–Riesz capacity , f-energy , image set , Lévy process

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 4 • July 2006
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