Moment-based approximation for variance of semi-Markovian random walk with gamma distributed interference of chance

Creative Commons License

Alakoç B., Kamişlik A. B., YAZIR T., Khaniyev T.

TURKISH JOURNAL OF MATHEMATICS, vol.48, no.6, pp.1037-1054, 2024 (SCI-Expanded) identifier identifier

  • Nəşrin Növü: Article / Article
  • Cild: 48 Say: 6
  • Nəşr tarixi: 2024
  • Doi nömrəsi: 10.55730/1300-0098.3559
  • jurnalın adı: TURKISH JOURNAL OF MATHEMATICS
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Səhifə sayı: pp.1037-1054
  • Açar sözlər: Semi-Markovian random walk process, moment-based approximation, ergodic distribution, boundary functional, interference of chance
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

This study proposed moment-based approximations for the expected value and variance of the ergodic distribution of the semi-Markovian random walk process (X(t)) with gamma distributed interference of chance. Many studies have investigated analogous moment problems by using an asymptotic approach. The key distinguishing aspect of this study from others in the literature is obtaining Kambo’s approximations for the moments of X(t) instead of asymptotic expansions. Firstly, the approximation formulas for the moments of boundary functional SN(z) of X(t) were obtained. Then using these results, approximation formulas for the first two moments of the ergodic distributions of X(t) were derived. Finally, the expected value and variance of X(t) were calculated by using the Monte Carlo simulation method for two concrete distributions (Gaussian and Uniform).