Bertoin, J.; van Harn, K.; Steutel, F. W. Renewal theory and level passage by subordinators. (English) Zbl 0965.60053 Stat. Probab. Lett. 45, No. 1, 65-69 (1999). Renewal processes (nondecreasing partial-sum processes) generated by infinitely divisible life times are used as stepping stones between general nondecreasing partial-sum processes and nondecreasing Lévy processes (subordinators). In this way the limit distributions are conjectured of the ‘undershoot’ and ‘overshoot’ at the passage of a high level by subordinators. These conjectures are then proved by Lévy-process methods. Reviewer: F.W.Steutel (Eindhoven) Cited in 25 Documents MSC: 60G51 Processes with independent increments; Lévy processes 60K05 Renewal theory 60E07 Infinitely divisible distributions; stable distributions Keywords:infinite divisibility; renewal theory; Lévy processes × Cite Format Result Cite Review PDF Full Text: DOI Link References: [1] Bertoin, J., 1996. Lévy Processes. Cambridge University Press, Cambridge.; Bertoin, J., 1996. Lévy Processes. Cambridge University Press, Cambridge. · Zbl 0861.60003 [2] Feller, W., 1971. An Introduction to Probability Theory and its Applications, vol. 2, second ed. Wiley, New York.; Feller, W., 1971. An Introduction to Probability Theory and its Applications, vol. 2, second ed. Wiley, New York. · Zbl 0219.60003 [3] van Harn, K.; Steutel, F. W., Infinite divisibility and the waiting-time paradox, Commun. Statist. Stochastic Models, 11, 3, 527-540 (1995) · Zbl 0843.60020 [4] Winter, B. B., Joint simulation of backward and forward recurrence times in a renewal process, J. Appl. Prob., 26, 404-407 (1989) · Zbl 0676.60081 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.