Some results on a stochastic process with a discrete chance interference

Abstract

In this study, some problems connected with stochastic process with a discrete chance interference X(t) are investigated. In particular, one-dimensional distribution functions of the process are obtained and under some weak assumptions, the ergodic theorem for this process is given. As a result, the explicit form of ergodic distribution function is derived. Moreover, the double transform of distribution function of additive functional of the process X(t) is derived Furthermore, asymptotic behaviour of the additive functional is investigated, as $t\rightarrow\infty$. Based on these results characteristic function of ergodic distribution of the process X(t) is obtained by using a joint distribution of random variables N and $S_N$ . In addition, the first and second moments of ergodic distribution of X(t) are expressed in terms of the moments of random variable N .