Asymptotic expansions for the moments of the boundary functionals of the renewal reward process with a discrete interference of chance

Aliyev R., Okur Bekar N., Xanıyev T., Unver I.

Mathematical and Computational Applications, vol.15, no.1, pp.117-126, 2010 (Scopus, TRDizin) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 15 Say: 1
  • Nəşr tarixi: 2010
  • Doi nömrəsi: 10.3390/mca15010117
  • jurnalın adı: Mathematical and Computational Applications
  • Jurnalın baxıldığı indekslər: Scopus, TR DİZİN (ULAKBİM)
  • Səhifə sayı: pp.117-126
  • Açar sözlər: Asymptotic expansion, Boundary functional, Discrete interference of chance, Laplace transform, Monte Carlo method, Renewal reward process
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

In this study, two boundary functionals N1 and τ1 of the renewal reward process with a discrete interference of chance (X(t) ) are investigated. A relation between the moment generating function (Χ N (z)) of the boundary functional N1 and the Laplace transform (Φτ ( μ)) of the boundary functional τ1 is obtained. Using this relation, the exact formulas for the first four moments of the boundary functional τ1 are expressed by means of the first four moments of the boundary functional N1. Moreover, the asymptotic expansions for the first four moments of these boundary functionals are established when the random variables {ζn}, n ≤ 0, which describe a discrete interference of chance, have an exponential distribution with parameter λ< 0. Finally, the accuracy of the approximation formulas for the moments (EN1k) of the boundary functional N1 are tested by Monte Carlo simulation method. © Association for Scientific Research.