Proper two-sided exits of a Lévy process

2015/11/24 by Matija Vidmar, Vidmar, Matija
Business, Management and Accounting · Computer Science · Mathematics · #Advanced Queuing Theory Analysis #Cellular Automata and Applications #FOS: Mathematics #Primary: 60G51 #Probability (math.PR) #Secondary: 60J75 #Stochastic processes and statistical mechanics #math.PR #msc:60G51 #msc:60J75

paper · pdf · doi:10.48550/arxiv.1511.07755

6 pages

arxiv created 2015/11/24 · openalex publication_date 2015/11/24 · arxiv updated 2015/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that the two-sided exits of a Levy process are proper, i.e. not a.s. equal to their one-sided counterparts, if and only if said process is not a subordinator or the negative of a subordinator. Furthermore, Levy processes are characterized, for which the supports of the first exit times from bounded annuli, simultaneously on each of the two events corresponding to exit at the lower and the upper boundary, respectively are unbounded, contain 0, are equal to [0,∞).

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