Hanalioglu, Z.Khaniyev, T.Agakishiyev, I.2024-09-292024-09-2920152146-1147https://hdl.handle.net/20.500.14619/8429In 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.eninfo:eu-repo/semantics/closedAccessRandom walkdiscrete interference of chancenormal distributionergodic distributionweak convergenceArticle731615WOS:000374003500006N/A