Three-term Asymptotic Expansion for the Moments of the Ergodic Distribution of a Renewal-reward Process with Gamma Distributed Interference of Chancea

Bekar N. O., Aliyev R., Khaniyev T.

1st International Conference on Analysis and Applied Mathematics (ICAAM), Gümüşhane, Turkey, 18 - 21 October 2012, vol.1470, pp.207-210 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1470
  • Doi Number: 10.1063/1.4747676
  • City: Gümüşhane
  • Country: Turkey
  • Page Numbers: pp.207-210
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this study, a renewal-reward process with a discrete interference of chance ( X(t)) is investigated. We assume that (X-lambda ( t))(t >= 0) is a renewal-reward process with a gamma distributed interference of chance with parameters (alpha, lambda), alpha > 0, lambda > 0. Under the assumption that the process is ergodic, the paper provides for each alpha > 1 the asymptotic expansions for the moments, the skewness (gamma(3)) and kurtosis (gamma(4)) of the process X-lambda, as lambda -> 0.