Gaussian Processes and Local Times of Symmetric Lévy Processes

Michael B. Marcus () and Jay Rosen ()
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Michael B. Marcus: City College, CUNY, Department of Mathematics
Jay Rosen: College of Staten Island, CUNY, Department of Mathematics

A chapter in Lévy Processes, 2001, pp 67-88 from Springer

Abstract: Abstract We give a relatively simple proof of the necessary and sufficient condition for the joint continuity of the local times of symmetric Lévy processes. This result was obtained in 1988 by M. Barlow and J. Hawkes without requiring that the Lévy processes be symmetric. In 1992 the authors used a very different approach to obtain necessary and sufficient condition for the joint continuity of the local times of strongly symmetric Markov processes, which includes symmetric Lévy processes. Both the 1988 proof and the 1992 proof are long and difficult. In this paper the 1992 proof is significantly simplified. This is accomplished by using two recent isomorphism theorems, which relate the local times of strongly symmetric Markov processes to certain Gaussian processes, one due to N. Eisenbaum alone and the other to N. Eisenbaum, H. Kaspi, M. B. Marcus, J. Rosen, and Z. Shi. Simple proofs of these isomorphism theorems are given in this paper.

Keywords: Markov Process; Local Time; Gaussian Process; Markov Property; Exponential Random Variable (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0197-7_4

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DOI: 10.1007/978-1-4612-0197-7_4

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