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2006 Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes
Yuji Kasahara, Shinzo Watanabe
Illinois J. Math. 50(1-4): 515-539 (2006). DOI: 10.1215/ijm/1258059484

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.

Citation

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Yuji Kasahara. Shinzo Watanabe. "Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes." Illinois J. Math. 50 (1-4) 515 - 539, 2006. https://doi.org/10.1215/ijm/1258059484

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1102.60066
MathSciNet: MR2247838
Digital Object Identifier: 10.1215/ijm/1258059484

Subjects:
Primary: 60J55
Secondary: 60G51, 60G52, 60J60

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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