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, cilt.39, ss.130-143, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 39 Konu: 1
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1080/03610920802662150
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Sayfa Sayıları: ss.130-143

Özet

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.