TY  - JOUR
TI  - WEAK CONVERGENCE THEOREM FOR THE ERGODIC DISTRIBUTION OF A RANDOM WALK WITH NORMAL DISTRIBUTED INTERFERENCE OF CHANCE
AB  - 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 ζn, 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, σ2). 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 Wa(t) ≡ X(t)/a is proved under additional condition that σ/a → 0 when a → ∞.
AU  - HANALIOGLU, Z.
AU  - KHANIYEV, T.
AU  - AGAKISHIYEV, I.
PY  - 2015
JO  - TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics
VL  - 5
IS  - 1
SN  - 2146-1147
SP  - 61
EP  - 73
DB  - TRDizin
UR  - http://search/yayin/detay/192511
ER  -