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2016 Deterministic time intervals on which a class of persistent processes are away from their origins
K. Bruce Erickson
Electron. Commun. Probab. 21: 1-12 (2016). DOI: 10.1214/16-ECP4688

Abstract

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.

Citation

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K. Bruce Erickson. "Deterministic time intervals on which a class of persistent processes are away from their origins." Electron. Commun. Probab. 21 1 - 12, 2016. https://doi.org/10.1214/16-ECP4688

Information

Received: 5 November 2015; Accepted: 25 July 2016; Published: 2016
First available in Project Euclid: 12 September 2016

zbMATH: 1348.60052
MathSciNet: MR3548774
Digital Object Identifier: 10.1214/16-ECP4688

Subjects:
Primary: 60F20, 60G50, 60J60, 60J65
Secondary: 60J55, 60K99

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