Illinois Journal of Mathematics

Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes

Yuji Kasahara and Shinzo Watanabe

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Abstract

It is well known that a class of subordinators can be represented using the local time of Brownian motions. An extension of such a representation is given for a class of Lévy processes which are not necessarily of bounded variation. This class can be characterized by the complete monotonicity of the Lévy measures. The asymptotic behavior of such processes is also discussed and the results are applied to the generalized arc-sine law, an occupation time problem on the positive side for one-dimensional diffusion processes.

Article information

Source
Illinois J. Math., Volume 50, Number 1-4 (2006), 515-539.

Dates
First available in Project Euclid: 12 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258059484

Digital Object Identifier
doi:10.1215/ijm/1258059484

Mathematical Reviews number (MathSciNet)
MR2247838

Zentralblatt MATH identifier
1102.60066

Subjects
Primary: 60J55: Local time and additive functionals
Secondary: 60G51: Processes with independent increments; Lévy processes 60G52: Stable processes 60J60: Diffusion processes [See also 58J65]

Citation

Kasahara, Yuji; Watanabe, Shinzo. Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes. Illinois J. Math. 50 (2006), no. 1-4, 515--539. doi:10.1215/ijm/1258059484. https://projecteuclid.org/euclid.ijm/1258059484


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