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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 463857, 12 pages
http://dx.doi.org/10.1155/2013/463857
Research Article

On the Laws of Total Local Times for -Paths and Bridges of Symmetric Lévy Processes

1Faculty of Science, University of the Ryukyus, 1 Senbaru, Okinawa, Nishihara 903-0213, Japan
2Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan

Received 12 May 2012; Accepted 29 November 2012

Academic Editor: Dumitru Baleanu

Copyright © 2013 Masafumi Hayashi and Kouji Yano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The joint law of the total local times at two levels for -paths of symmetric Lévy processes is shown to admit an explicit representation in terms of the laws of the squared Bessel processes of dimensions two and zero. The law of the total local time at a single level for bridges is also discussed.