Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1998; 35(1): 207-224

Printed March 1, 1998

Copyright © The Korean Mathematical Society.

On selfsimilar and semi-selfsimilar processes with independent increments

Ken-iti Sato and Kouji Yamamuro

Konan Women's Junior College

Abstract

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

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