Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance


Khaniyev T., KESEMEN T., Aliyev R., KOKANGÜL A.

STATISTICS & PROBABILITY LETTERS, vol.78, no.6, pp.785-793, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 78 Issue: 6
  • Publication Date: 2008
  • Doi Number: 10.1016/j.spl.2007.09.045
  • Journal Name: STATISTICS & PROBABILITY LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.785-793
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, a semi-Markovian random walk process (X(t)) with a discrete interference of chance is constructed and the ergodicity of this process is discussed. Some exact formulas for the first- and second-order moments of the ergodic distribution of the process X(t) are obtained, when the random variable zeta(1) has an exponential distribution with the parameter lambda > 0. Here zeta(1) expresses the quantity of a discrete interference of chance. Based on these results, the third-order asymptotic expansions for mathematical expectation and variance of the ergodic distribution of the process X(t) are derived, when lambda -> 0. (c) 2007 Elsevier B.V. All rights reserved.