Weak Convergence Theorem For A Semi-Markovian Random Walk With Delay And Pareto Distributed Interference Of Chance

KESEMEN T., Yetim F.

1st International Conference on Analysis and Applied Mathematics (ICAAM), Gümüşhane, Turkey, 18 - 21 October 2012, vol.1470, pp.255-258 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1470
  • Doi Number: 10.1063/1.4747689
  • City: Gümüşhane
  • Country: Turkey
  • Page Numbers: pp.255-258
  • Karadeniz Technical University Affiliated: Yes

Abstract

A semi-Markovian random walk with delay and a discrete interference of chance (X(t)) is constructed. The weak convergence theorem is proved for the ergodic distribution of the process X(t) and the limit form of the ergodic distribution is found, when the random variables {zeta(n)}, n >= 0 have Pareto distribution with parameters (alpha, lambda), where the random variables zeta(n) describe the discrete interference of chance.