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February 2019 Inventory model of type $(s,S)$ under heavy tailed demand with infinite variance
Aslı Bektaş Kamışlık, Tülay Kesemen, Tahir Khaniyev
Braz. J. Probab. Stat. 33(1): 39-56 (February 2019). DOI: 10.1214/17-BJPS376


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.


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Aslı Bektaş Kamışlık. Tülay Kesemen. Tahir Khaniyev. "Inventory model of type $(s,S)$ under heavy tailed demand with infinite variance." Braz. J. Probab. Stat. 33 (1) 39 - 56, February 2019.


Received: 1 September 2016; Accepted: 1 September 2017; Published: February 2019
First available in Project Euclid: 14 January 2019

zbMATH: 07031063
MathSciNet: MR3898721
Digital Object Identifier: 10.1214/17-BJPS376

Keywords: asymptotic expansion , heavy tailed distributions with infinite variance , Karamata theorem , regular variation , renewal reward process , Semi-Markovian inventory model of type $(s,S)$

Rights: Copyright © 2019 Brazilian Statistical Association


Vol.33 • No. 1 • February 2019
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