The Dichotomy of Recurrence and Transience of Semi-Lévy Processes

Makoto Maejima (), Taisuke Takamune and Yohei Ueda ()
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Makoto Maejima: Keio University
Taisuke Takamune: Keio University
Yohei Ueda: Keio University

Journal of Theoretical Probability, 2014, vol. 27, issue 3, 982-996

Abstract: Abstract A semi-Lévy process is an additive process with periodically stationary increments. In particular, it is a generalization of a Lévy process. The dichotomy of recurrence and transience of Lévy processes is well known, but this is not necessarily true for general additive processes. In this paper, we prove the recurrence and transience dichotomy of semi-Lévy processes. For the proof, we introduce a concept of semi-random walk and discuss its recurrence and transience properties. An example of semi-Lévy process constructed from two independent Lévy processes is investigated. Finally, we prove the laws of large numbers for semi-Lévy processes.

Keywords: Lévy process; Semi-Lévy process; Recurrence; Transience; Semi-random walk; Law of large numbers; 60G51 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0452-1

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