文章基本信息

标题：Deterministic time intervals on which a class of persistent processes are away from their origins
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作者：K. Bruce Erickson
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2016
卷号：21
DOI：10.1214/16-ECP4688
语种：English
出版社：Electronic Communications in Probability
摘要：There are three results each concerning large but remote deterministic time intervals at which excursions of a process away from the origin must occur. The first result gives a sufficient condition for a persistent random walk with a finite fourth moment. In this instance the aforementioned time intervals include an additional requirement that the walk is far away from the origin. The second result gives a necessary and a sufficient condition for similar excursions in the case of Brownian motion. The third result gives a necessary and a sufficient condition for time intervals to be free of the zeros of a class of persistent natural scale linear diffusions on the line and is equivalent to the determination of recurrent sets at infinity of the inverse local time.