ASYMPTOTIC EXPANSIONS FOR THE MOMENTS OF THE RENEWAL-REWARD PROCESS WITH A NORMAL DISTRIBUTED INTERFERENCE OF CHANCE

Hanalioglu Z., Fescioglu Unver N., Xanıyev T.

Applied and Computational Mathematics, vol.17, no.2, pp.141-150, 2018 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 17 Say: 2
  • Nəşr tarixi: 2018
  • jurnalın adı: Applied and Computational Mathematics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.141-150
  • Açar sözlər: Asymptotic Expansion, Discrete Interference of Chance, Ergodic Moments, Monte Carlo Simulation Method, Renewal-Reward Process
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

In this study, a renewal-reward process with a normal distributed interference of chance is mathematically constructed. The ergodicity of this process is discussed. The exact formulas for the nth order moments of the ergodic distribution of the process are obtained, when the interference of chance has a truncated normal distribution with parameters (a, σ2). Using these results, we derive the asymptotic expansions with three terms for the nth order moments of the ergodic distribution, when a → ∞. Finally, the accuracy of the approximation formulas for the nth order moments of the ergodic distribution are tested by the Monte Carlo simulation method.