Asymptotic Expansions for the Moments of the Semi-Markovian Random Walk with Gamma Distributed Interference of Chance


Aliyev R., Khaniyev T., KESEMEN T.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.39, no.1, pp.130-143, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.1080/03610920802662150
  • Title of Journal : COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Page Numbers: pp.130-143

Abstract

In this study, a semi-Markovian random walk with a discrete interference of chance (X(t)) is considered and under some weak assumptions the ergodicity of this process is discussed. The exact formulas for the first four moments of the ergodic distribution of the process X(t) are obtained when the random variable zeta(1), which describes a discrete interference of chance, has a gamma distribution with parameters (alpha, lambda), alpha > 1, lambda > 0. Based on these results, the asymptotic expansions are obtained for the first four moments of the ergodic distribution of the process X(t), as lambda -> 0. Furthermore, the asymptotic expansions for the skewness and kurtosis of the ergodic distribution of the process X(t) are established. Finally, it is discussed that the alternative estimations for the stationary characteristics of this process can be offered by using obtained asymptotic expansions.