Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 50, Number 1-4 (2006), 515-539.
Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes
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.
Illinois J. Math., Volume 50, Number 1-4 (2006), 515-539.
First available in Project Euclid: 12 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J55: Local time and additive functionals
Secondary: 60G51: Processes with independent increments; Lévy processes 60G52: Stable processes 60J60: Diffusion processes [See also 58J65]
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