unimodal lévy process
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1993 ◽  
Vol 132 ◽  
pp. 141-153 ◽  
Author(s):  
Toshiro Watanabe

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.


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