ON THE SEMI-MARKOVIAN RANDOM WALK WITH DELAY AND WEIBULL DISTRIBUTED INTERFERENCE OF CHANCE


Kesemen T.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.42, no.3, pp.299-307, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2013
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.299-307

Abstract

In this paper, a semi-Markovian random walk with delay and a discrete interference of chance (X(t)) is considered. It is assumed that the random variables {zeta(n)}, n >= 1 which describe the discrete interference of chance have Weibull distribution with parameters (alpha, lambda), alpha > 1, lambda > 0. Under this assumption, the ergodicity of this process is discussed and the asymptotic expansions with three terms for the first four moments of the ergodic distribution of the process X(t) are derived, when lambda -> 0. Moreover, the asymptotic expansions for the skewness and kurtosis of the ergodic distribution of the process X(t) are established.