Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/2974
Title: Inventory model of type (s, S) under heavy tailed demand with infinite variance
Authors: Kamışlık, Aslı Bektaş
Kesemen, Tülay
Khaniyev, Tahir
17222
Keywords: Semi-Markovian inventory model of type (s, S)
heavy tailed distributions with infinite variance
regular variation
renewal reward process
asymptotic expansion
Karamata theorem
Issue Date: 2019
Publisher: Brazilian Statistical Association
Source: Kamışlık, A. B., Kesemen, T., & Khaniyev, T. (2019). Inventory model of type $(s, S) $ under heavy tailed demand with infinite variance. Brazilian Journal of Probability and Statistics, 33(1), 39-56.
Abstract: In this study, a stochastic process X(t), which describes an inventory model of type (s, S) is considered in the presence of heavy tailed demands with infinite variance. The aim of this study is observing the impact of regularly varying demand distributions with infinite variance on the stochastic process X(t). The main motivation of this work is, the publication by Geluk [Proceedings of the American Mathematical Society 125 (1997) 3407-3413] where he provided a special asymptotic expansion for renewal function generated by regularly varying random variables. Two term asymptotic expansion for the ergodic distribution function of the process X(t) is obtained based on the main results proposed by Geluk [Proceedings of the American Mathematical Society 125 (1997) 3407-3413]. Finally, weak convergence theorem for the ergodic distribution of this process is proved by using Karamata theory.
URI: https://hdl.handle.net/20.500.11851/2974
https://projecteuclid.org/euclid.bjps/1547456486
https://doi.org/10.1214/17-BJPS376
ISSN: 0103-0752
Appears in Collections:Endüstri Mühendisliği Bölümü / Department of Industrial Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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