Limit theorem for a semi - Markovian stochastic model of type (s,S)

Authors : Zulfiye Hanalioglu, Tahir Khaniyev

Pages : 605-615

View : 22 | Download : 11

Publication Date : 2019-04-01

Article Type : Research

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 $W(t)\equiv (2X(t)) / (S-s)$. 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.
Keywords : Inventory model of type $(s, S)$, Renewal-reward process, Weak convergence, Asymmetric triangular distribution, Asymptotic expansion