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Lower functions for processes with stationary independent increments

Authors:	In-Suk Wee

Institution:	(1) Department of Mathematics, Korea University, Seoul, Korea

Abstract:	Summary Let {X _t} be aR ¹-valued process with stationary independent increments and $A_t = \mathop {\sup }\limits_{s \leqq t} \|X_s \|$ . In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing functionh(t) such that lim infA _t/h(t)=C a.s. ast0 andt, for some positive finite constantC whenh(t) takes a particular form. Also two analytic conditions are considered as application.This research is partially supported by Korea Science & Engineering Foundation

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