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https://hdl.handle.net/20.500.11851/2975
Title: | Limit Theorem for a Semi - Markovian Stochastic Model of Type (s,s) | Authors: | Hanalioğlu, Zülfiye Khaniyev, Tahir |
Keywords: | Inventory model of type (s,S) renewal-reward process weak convergence asymmetric triangular distribution asymptotic expansion |
Publisher: | Hacettepe University | Source: | Hanalioglu, Z., & Khaniyev, T. (2019). Limit theorem for a semi-Markovian stochastic model of type (s, S). Hacettepe Journal of Mathematics and Statistics, 48(2), 605-615. | Abstract: | In this study, a semi-Markovian inventory model of type (s,S) is considered and the model is expressed by means of renewal-reward process (X(t)) with an asymmetric triangular distributed interference of chance and delay. The ergodicity of the process X(t) is proved and the exact expression for the ergodic distribution is obtained. Then, two-term asymptotic expansion for the ergodic distribution is found for standardized process W(t) equivalent to (2X(t))/(S - s). Finally, using this asymptotic expansion, the weak convergence theorem for the ergodic distribution of the process W(t) is proved and the explicit form of the limit distribution is found. | URI: | https://search.trdizin.gov.tr/yayin/detay/296627 https://hdl.handle.net/20.500.11851/2975 https://dergipark.org.tr/tr/login https://doi.org/10.15672/HJMS.2018.622 |
ISSN: | 1303-5010 |
Appears in Collections: | Endüstri Mühendisliği Bölümü / Department of Industrial Engineering Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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