J. Korean Math. Soc. 1998; 35(1): 207-224
Printed March 1, 1998
Copyright © The Korean Mathematical Society.
Ken-iti Sato and Kouji Yamamuro
Konan Women's Junior College
After the review of known results on the connections between selfsimilar processes with independent increments (processes of class $L$) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecom- posable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bounded sets. Comparison in transience-recurrence of the L\'evy process and the process of class $L$ associated with a common distribution of class $L$ is made.
Keywords: selfsimilar, semi-selfsimilar, selfdecomposable, semi-selfdecomposable, independent increments, L\'evy process, additive process, process of class $L$, transience, recurrence
MSC numbers: 60G18, 60J30
1998; 35(3): 783-791
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