Brownian representation of a class of Levy 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 Levy processes which are not necessarily of bounded variation. This class can be characterized by the complete monotonicity of the Levy 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.