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Renewal theory and level passage by subordinators

Author

Listed:
  • Bertoin, J.
  • van Harn, K.
  • Steutel, F. W.

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.

Suggested Citation

  • Bertoin, J. & van Harn, K. & Steutel, F. W., 1999. "Renewal theory and level passage by subordinators," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 65-69, October.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:1:p:65-69
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    Citations

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    Cited by:

    1. Chi, Zhiyi, 2016. "On exact sampling of the first passage event of a Lévy process with infinite Lévy measure and bounded variation," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1124-1144.
    2. Ghorbel, M. & Huillet, T., 2005. "Fragment size distributions in random fragmentations with cutoff," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 47-60, January.
    3. Mijatović, Aleksandar & Pistorius, Martijn, 2015. "Buffer-overflows: Joint limit laws of undershoots and overshoots of reflected processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2937-2954.
    4. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    5. Budd, J.K. & Taylor, P.G., 2019. "Bounds for the solution to the single-period inventory model with compound renewal process input: An application to setting credit card limits," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1012-1018.
    6. Huillet, Thierry & Möhle, Martin, 2013. "On the extended Moran model and its relation to coalescents with multiple collisions," Theoretical Population Biology, Elsevier, vol. 87(C), pages 5-14.

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