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Oscillation of modes of some semi-stable Lévy processes

Published online by Cambridge University Press:  22 January 2016

Toshiro Watanabe
Toshiro Watanabe*
Affiliation:
Center for Mathematical Sciences, The University of Aizu, IkkimachiAizuwakamatsu, Fukushima, 965, Japan
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In this paper it is shown that there is a unimodal Levy process with oscillating mode. After the author first constructed an example of such a self-decomposable process, Sato pointed out that it belongs to the class of semi-stable processes with β < 0. We prove that all non-symmetric semi-stable self-decomposable processes with β < 0 have oscillating modes.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 132 , December 1993 , pp. 141 - 153
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

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