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On the use of Lyapunov function methods in renewal theory

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  • Konstantopoulos, Takis
  • Last, Günter

Abstract

Based on recent results on the exploitation of "drift criteria" for general state-space Markov processes, we derive rates of convergence for (moments of ) processes associated with a renewal process with common inter-renewal time distribution F. Some of the results are classical and some are new, but the proofs are novel and, we believe, useful if one needs to derive convergence results based on the exact form of the tail of F, a typical concern in applications such as implications of long-range dependence in performance of networking systems, reliability analysis or risk theory.

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  • 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.
    • Handle: RePEc:eee:spapps:v:79:y:1999:i:1:p:165-178
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    References listed on IDEAS

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    1. Alsmeyer, Gerold, 1996. "Superposed continuous renewal processes A Markov renewal approach," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 311-322, February.
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    Cited by:

    1. Ari Arapostathis & Hassan Hmedi & Guodong Pang, 2021. "On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 772-796, May.
    2. Patrice Bertail & Stéphan Clémençon & Jessica Tressou, 2006. "A Storage Model with Random Release Rate for Modeling Exposure to Food Contaminants," Working Papers 2006-20, Center for Research in Economics and Statistics.
    3. Robert Eymard & Sophie Mercier & Michel Roussignol, 2011. "Importance and Sensitivity Analysis in Dynamic Reliability," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 75-104, March.
    4. Itai Gurvich & Junfei Huang & Avishai Mandelbaum, 2014. "Excursion-Based Universal Approximations for the Erlang-A Queue in Steady-State," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 325-373, May.

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