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


HANALİOĞLU Z. , Khaniyev T.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.48, ss.605-615, 2019 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 48 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.15672/hjms.2018.622
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Sayfa Sayısı: ss.605-615

Özet

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.