WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE


Hanalioglu Z., Khaniyev T., Agakishiyev I.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, cilt.5, ss.61-73, 2015 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 5 Konu: 1
  • Basım Tarihi: 2015
  • Dergi Adı: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Sayfa Sayıları: ss.61-73

Özet

In this study, a semi-Markovian random walk process (X (t)) with a discrete interference of chance is investigated. Here, it is assumed that the zeta(n), n = 1; 2; 3, ..., which describe the discrete interference of chance are independent and identically distributed random variables having restricted normal distribution with parameters (a; sigma(2)). Under this assumption, the ergodicity of the process X (t) is proved. Moreover, the exact forms of the ergodic distribution and characteristic function are obtained. Then, weak convergence theorem for the ergodic distribution of the process W-a (t) = X (t) = a is proved under additional condition that sigma/a -> 0 when a -> infinity.