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Approximate formulas for renewal-reward process with dependent components and normally distributed interference of chance

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  • Poladova, Aynura
  • Tekin, Salih
  • Khaniyev, Tahir

Abstract

In this study a modification of renewal-reward process with dependent components and normally distributed interference of chance are investigated. The approximate formulas for the ergodic distribution of the process and its moments are proposed.

Suggested Citation

  • Poladova, Aynura & Tekin, Salih & Khaniyev, Tahir, 2025. "Approximate formulas for renewal-reward process with dependent components and normally distributed interference of chance," Statistics & Probability Letters, Elsevier, vol. 224(C).
    • Handle: RePEc:eee:stapro:v:224:y:2025:i:c:s0167715225000847
    DOI: 10.1016/j.spl.2025.110439
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    References listed on IDEAS

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    1. Khaniyev, T. & Kesemen, T. & Aliyev, R. & Kokangul, A., 2008. "Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 785-793, April.
    2. Khaniyev, Tahir & Kucuk, Zafer, 2004. "Asymptotic expansions for the moments of the Gaussian random walk with two barriers," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 91-103, August.
    3. Patch, Brendan & Nazarathy, Yoni & Taimre, Thomas, 2015. "A correction term for the covariance of renewal-reward processes with multivariate rewards," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 1-7.
    4. Aliyev, Rovshan & Bayramov, Veli, 2017. "On the asymptotic behaviour of the covariance function of the rewards of a multivariate renewal–reward process," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 138-149.
    5. Tahir Khaniyev & Ali Kokangul & Rovshan Aliyev, 2013. "An asymptotic approach for a semi‐Markovian inventory model of type (s, S)," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(5), pages 439-453, September.
    6. Rovshan Aliyev & Ozlem Ardic & Tahir Khaniyev, 2016. "Asymptotic approach for a renewal-reward process with a general interference of chance," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(14), pages 4237-4248, July.
    7. Zamparo, Marco, 2023. "Large deviation principles for renewal–reward processes," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 226-245.
    8. Brown, Mark & Solomon, Herbert, 1975. "A second-order approximation for the variance of a renewal reward process," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 301-314, July.
    9. Aynura Poladova & Salih Tekin & Tahir Khaniyev, 2020. "A novel replacement policy for a linear deteriorating system using stochastic process with dependent components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(3), pages 381-396, May.
    10. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
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