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Renewal theory and level passage by subordinators


Bertoin, Jean; van Harn, K; Steutel, F W (1999). Renewal theory and level passage by subordinators. Statistics and Probability Letters, 45(1):65-69.

Abstract

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, it is easy to conjecture the limit distributions of the ‘undershoot’ and ‘overshoot’ at the passage of a high level by subordinators. These conjectures are then proved by Lévy-process methods.

Abstract

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, it is easy to conjecture the limit distributions of the ‘undershoot’ and ‘overshoot’ at the passage of a high level by subordinators. These conjectures are then proved by Lévy-process methods.

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Citations

20 citations in Web of Science®
21 citations in Scopus®
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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1999
Deposited On:25 Jul 2013 06:43
Last Modified:05 Apr 2016 16:52
Publisher:Elsevier
ISSN:0167-7152
Publisher DOI:https://doi.org/10.1016/S0167-7152(99)00043-7
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1718352
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0965.60053

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