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Inventory model of type (s, S) under heavy tailed demand with infinite variance

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info:eu-repo/semantics/openAccess

Date

2019

Author

Kamışlık, Aslı Bektaş
Kesemen, Tülay
Khaniyev, Tahir

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Citation

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. https://doi.org/10.1214/17-BJPS376

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.

Source

Brazilian Journal of Probability and Statistics

Volume

33

Issue

1

URI

https://doi.org/10.1214/17-BJPS376
https://hdl.handle.net/11436/1599

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  • FEF, Matematik Bölümü Koleksiyonu [162]
  • Scopus İndeksli Yayınlar Koleksiyonu [6023]
  • WoS İndeksli Yayınlar Koleksiyonu [5260]



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