The class of L ∩ D and its application to renewal reward process

Kamişlik, Aslı Bektaş; Kesemen, Tülay; Khaniyev, Tahir

doi:10.1063/1.5020457

Cited by 2 publications

(1 citation statement)

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“…Furthermore, asymptotic expansion for ergodic distribution function of the process X(t) and asymptotic expansion for the moments of ergodic distribution were obtained. Bektaş et al [8] took L ∩ D subclass of heavy tailed distributions for demand random variables and provided asymptotic expansion for ergodic distribution function of the process. Besides, in publications by Bektaş et al [6,7] semi-Markovian inventory model of type (s, S) is considered with general class of regularly varying distributions with infinite variance, i.e.…”

Section: Introductionmentioning

confidence: 99%

A semi-Markovian renewal reward process withΓ(g)distributed demand

Kamişlik¹,

Alakoç²,

Kesemen³

et al. 2020

Turk J Math

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We consider a classical semi-Markovian stochastic model of type (s, S) with Logistic distributed demand random variables. Logistic distribution is a member of special distribution class known as Γ(g) that encounters in many real-life applications involving extreme value theory. The objective of this study is to observe some major characteristics of a stochastic process X(t) which represents semi-Markovian renewal reward process of type (s, S) .We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion for ergodic distribution function and for n th order moments of ergodic distribution of the process X(t) .

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Section: Introductionmentioning

confidence: 99%