Weak convergence theorem for ergodic distribution of stochastic processes with discrete interference of chance and generalized reflecting barrier

Abstract

In this paper, a stochastic process with discrete interference of chance and generalized reflecting barrier (X (t)) is constructed and the ergodicity of this process is proved. Using basic identity for random walk processes, a characteristic function of the ergodic distribution is written with the help of characteristics of the boundary functional S-N1(x). Moreover, a weak convergence theorem for the ergodic distribution of the standardized process Y-lambda(t) = X(t)/lambda is proved, as lambda -> infinity and the limit form of the ergodic distribution is found.

[Aliyev, R.] Baku State Univ, Dept Probabil Theory & Math Stat, Baku, Azerbaijan; [Aliyev, R.; Khaniyev, T.] Azerbaijan Natl Acad Sci, Inst Cybernet, Baku, Azerbaijan; [Khaniyev, T.; Gever, B.] TOBB Univ Econ & Technol, Dept Ind Engn, Ankara, Turkey