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

Hanalioglu Z., Khaniyev T.

Hacettepe Journal of Mathematics and Statistics, vol.48, no.2, pp.605-615, 2019 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 48 Say: 2
  • Nəşr tarixi: 2019
  • Doi nömrəsi: 10.15672/hjms.2018.622
  • jurnalın adı: Hacettepe Journal of Mathematics and Statistics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Səhifə sayı: pp.605-615
  • Açar sözlər: Asymmetric triangular distribution, Asymptotic expansion, Inventory model of type (s, Renewal-reward process, S), Weak convergence
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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) ≡ (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.