Some results on a stochastic process with a discrete chance interference (Q1586175)

Summary: Some problems connected with stochastic processes 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 the distribution function of the additive functional of the process \(X(t)\) is derived. Furthermore, the asymptotic behaviour of the additive functional is investigated as \(t\to\infty\). Based on these results the characteristic function of the 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 the ergodic distribution of \(X(t)\) are expressed in terms of the moments of the random variable \(N\).