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, cilt.78, ss.785-793, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 78 Konu: 6
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1016/j.spl.2007.09.045
  • Sayfa Sayıları: ss.785-793


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.