We establish the rate of convergence to the exponential distribution in the general limit theorem for the extreme values of regenerative processes. We also suggest some applications of this result to the birth and death processes and to the queue length processes.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 8, pp. 1064–1081, August, 2020. Ukrainian DOI: 10.37863/umzh.v72i8.1028.
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Zakusylo, O.K., Matsak, I.K. Estimation of the Rate of Convergence in the Limit Theorem for Extreme Values of Regenerative Processes. Ukr Math J 72, 1230–1250 (2021). https://doi.org/10.1007/s11253-020-01855-1
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DOI: https://doi.org/10.1007/s11253-020-01855-1