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Superposed continuous renewal processes A Markov renewal approach

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  • Alsmeyer, Gerold

Abstract

Lam and Lehoczky (1991) have recently given a number of extensions of classical renewal theorems to superpositions of p independent renewal processes. In this article we want to advertise an approach that more explicitly uses a Markov renewal theoretic framework and thus leads to a simplified derivation of their main results together with a number of new ones. Those include a Stone-type decomposition for the resulting Markov renewal measure and a number of convergence rate results which extend the corresponding results for single renewal processes.

Suggested Citation

  • Alsmeyer, Gerold, 1996. "Superposed continuous renewal processes A Markov renewal approach," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 311-322, February.
    • Handle: RePEc:eee:spapps:v:61:y:1996:i:2:p:311-322
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    References listed on IDEAS

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    1. Karl Sigman, 1990. "One-Dependent Regenerative Processes and Queues in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 175-189, February.
    2. Alsmeyer, Gerold, 1994. "On the Markov renewal theorem," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 37-56, March.
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    Cited by:

    1. Kella, Offer & Stadje, Wolfgang, 2006. "Superposition of renewal processes and an application to multi-server queues," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1914-1924, November.
    2. Stadje, Wolfgang, 2012. "Embedded Markov chain analysis of the superposition of renewal processes," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1497-1503.
    3. Zhao, Ruiqing & Tang, Wansheng & Yun, Huaili, 2006. "Random fuzzy renewal process," European Journal of Operational Research, Elsevier, vol. 169(1), pages 189-201, February.
    4. Konstantopoulos, Takis & Last, Günter, 1999. "On the use of Lyapunov function methods in renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 165-178, January.
    5. Alsmeyer, Gerold & Hoefs, Volker, 2002. "Markov renewal theory for stationary (m+1)-block factors: convergence rate results," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 77-112, March.
    6. Gerold Alsmeyer & Fabian Buckmann, 2018. "Fluctuation Theory for Markov Random Walks," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2266-2342, December.

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