The Annals of Probability

Level Sets of Additive Lévy Processes

Davar Khoshnevisan and Yimin Xiao

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Abstract

We provide a probabilistic interpretation of a class of natural capacities on Euclidean space in terms of the level sets of a suitably chosen multiparameter additive Lévy process X. We also present several probabilistic applications of the aforementioned potential-theoretic connections. They include areas such as intersections of Lévy processes and level sets, as well as Hausdorff dimension computations.

Article information

Source
Ann. Probab. Volume 30, Number 1 (2002), 62-100.

Dates
First available in Project Euclid: 29 April 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1020107761

Digital Object Identifier
doi:10.1214/aop/1020107761

Mathematical Reviews number (MathSciNet)
MR

Zentralblatt MATH identifier
1019.60049

Subjects
Primary: 60G60: Random fields
Secondary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
Additive stable processes potential theory

Citation

Khoshnevisan, Davar; Xiao, Yimin. Level Sets of Additive Lévy Processes. Ann. Probab. 30 (2002), no. 1, 62--100. doi:10.1214/aop/1020107761. http://projecteuclid.org/euclid.aop/1020107761.


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  • REDMOND, WASHINGTON 98052 E-MAIL: xiao@math.utah.edu