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

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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

  • Publication Type: Article / Article
  • Volume: 48 Issue: 6
  • Publication Date: 2024
  • Doi Number: 10.55730/1300-0098.3559
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.1037-1054
  • Keywords: Semi-Markovian random walk process, moment-based approximation, ergodic distribution, boundary functional, interference of chance
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

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).