SOME ASYMPTOTIC RESULTS FOR A SEMI-MARKOVIAN RANDOM WALK WITH A SPECIAL BARRIER


Aliyev R., KESEMEN T. , Khaniyev T.

PAKISTAN JOURNAL OF STATISTICS, cilt.30, ss.411-428, 2014 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 30 Konu: 3
  • Basım Tarihi: 2014
  • Dergi Adı: PAKISTAN JOURNAL OF STATISTICS
  • Sayfa Sayıları: ss.411-428

Özet

In this paper, a semi-Markovian random walk with a discrete interference of chance (X(t)) is considered. Under the assumption that the random variables {zeta(n)}, n >= 1 describing discrete interference of chance are in the form of an ergodic Markov chain with Weibull stationary distribution, the ergodic theorem for the process X(t) is proved. By using basic identity, the characteristic function of the process X(t) is expressed by the characteristics of a boundary functional S-N(x). Moreover, the asymptotic expansions with three terms for the first four moments of the ergodic distribution of the process X(t) are obtained, when the expected value of the jump at time of discrete interference of chance tends to infinity.